---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '21718'
abstract:
- lang: eng
text: "In this paper, we consider the big algebra recently introduced by Hausel
for the GLn-action on the coordinate ring of the matrix space Mat(n,r). In particular,
we obtain explicit formulas for the big algebra generators in terms of differential
operators with polynomial coefficients. We show that big algebras in type A are
commutative and relate them to the Bethe subalgebra in the Yangian Y(gln). We
apply these results to big algebras of symmetric powers of the standard representation
of GLn.\r\n."
acknowledgement: "I would like to express my gratitude to Tam´as Hausel for introducing
me to the subject and\r\nfor his constant guidance throughout this work. I would
also like to thank Tam´as Hausel,\r\nMischa Elkner, Jakub L¨owit, Anton Mellit,
Marino Romero, Leonid Rybnikov for many fruitful\r\ndiscussions and feedback on
earlier drafts of this paper. We are grateful to the anonymous\r\nreferees for many
useful comments and suggestions that improved the manuscript. This work was done
during the author’s PhD studies at the Institute of Science and Technology Austria
(ISTA). The author was supported by the Austrian Science Fund (FWF) grant\r\n“Geometry
of the tip of the global nilpotent cone” no. 10.55776/P35847 and the DOC Fellowship
of the Austrian Academy of Sciences. The author also acknowledges the long-term
program\r\nof support of the Ukrainian research teams at the Polish Academy of Sciences
carried out in\r\ncollaboration with the U.S. National Academy of Sciences with
the financial support of external\r\npartners. For open access purposes, the author
has applied a CC BY public copyright license\r\nto any author-accepted manuscript
version arising from this submission."
article_number: '024'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nhok T
full_name: Ngo, Nhok T
id: 28e53c8c-896a-11ed-bdf8-f809043ce2f0
last_name: Ngo
citation:
ama: 'Ngo NT. Big algebra in type A for the coordinate ring of the matrix space.
Symmetry, Integrability and Geometry: Methods and Applications. 2026;22.
doi:10.3842/SIGMA.2026.024'
apa: 'Ngo, N. T. (2026). Big algebra in type A for the coordinate ring of the matrix
space. Symmetry, Integrability and Geometry: Methods and Applications.
National Academy of Science of Ukraine. https://doi.org/10.3842/SIGMA.2026.024'
chicago: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
Space.” Symmetry, Integrability and Geometry: Methods and Applications.
National Academy of Science of Ukraine, 2026. https://doi.org/10.3842/SIGMA.2026.024.'
ieee: 'N. T. Ngo, “Big algebra in type A for the coordinate ring of the matrix space,”
Symmetry, Integrability and Geometry: Methods and Applications, vol. 22.
National Academy of Science of Ukraine, 2026.'
ista: 'Ngo NT. 2026. Big algebra in type A for the coordinate ring of the matrix
space. Symmetry, Integrability and Geometry: Methods and Applications. 22, 024.'
mla: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
Space.” Symmetry, Integrability and Geometry: Methods and Applications,
vol. 22, 024, National Academy of Science of Ukraine, 2026, doi:10.3842/SIGMA.2026.024.'
short: 'N.T. Ngo, Symmetry, Integrability and Geometry: Methods and Applications
22 (2026).'
corr_author: '1'
date_created: 2026-04-12T22:01:51Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-04-16T06:11:12Z
day: '14'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.3842/SIGMA.2026.024
external_id:
arxiv:
- '2501.04605'
file:
- access_level: open_access
checksum: 29b28b5f8717ed1a084a2b551d0fd284
content_type: application/pdf
creator: dernst
date_created: 2026-04-16T06:06:54Z
date_updated: 2026-04-16T06:06:54Z
file_id: '21740'
file_name: 2026_SIGMA_Ngo.pdf
file_size: 975460
relation: main_file
success: 1
file_date_updated: 2026-04-16T06:06:54Z
fulldoi: https://doi.org/10.3842/SIGMA.2026.024
has_accepted_license: '1'
intvolume: ' 22'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
- _id: e6c64f42-ab3c-11f0-94c7-a95658059ccc
grant_number: '27483'
name: Big algebras in classical types
publication: 'Symmetry, Integrability and Geometry: Methods and Applications'
publication_identifier:
eissn:
- 1815-0659
publication_status: published
publisher: National Academy of Science of Ukraine
quality_controlled: '1'
scopus_import: '1'
status: public
title: Big algebra in type A for the coordinate ring of the matrix space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '21489'
abstract:
- lang: eng
text: We study Kirillov algebras attached to minuscule highest weight representations
of semisimple Lie algebras. They can be viewed as equivariant cohomology algebras
of partial flag varieties. Real structures on the varieties then induce involutions
of these algebras. We describe how these involutions act on the spectra of minuscule
Kirillov algebras, and model the fixed points via the equivariant cohomology of
real partial flag varieties. We then use this model to characterise freeness of
the fixed point coordinate ring over the appropriate base. As an application,
we recover a q = -1 phenomenon of Stembridge in the minuscule case by geometric
means.
acknowledgement: 'I would like to thank Tamás Hausel for introducing me to this area
of mathematics and for his constant guidance. I would also like to thank Jakub Löwit
and Miguel González for fruitful discussions and many helpful comments on this paper.
This work was done during the author’s PhD studies at the Institute of Science and
Technology Austria (ISTA). It was funded by the Austrian Science Fund (FWF) 10.55776/P35847.
Open access funding provided by Institute of Science and Technology (IST Austria). '
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Mischa M
full_name: Elkner, Mischa M
id: 477faa59-080d-11ed-979a-c693ab7638ab
last_name: Elkner
citation:
ama: Elkner MM. On involutions of minuscule Kirillov algebras induced by real structures.
Transformation Groups. 2026. doi:10.1007/s00031-026-09958-y
apa: Elkner, M. M. (2026). On involutions of minuscule Kirillov algebras induced
by real structures. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-026-09958-y
chicago: Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced
by Real Structures.” Transformation Groups. Springer Nature, 2026. https://doi.org/10.1007/s00031-026-09958-y.
ieee: M. M. Elkner, “On involutions of minuscule Kirillov algebras induced by real
structures,” Transformation Groups. Springer Nature, 2026.
ista: Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by
real structures. Transformation Groups.
mla: Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced by
Real Structures.” Transformation Groups, Springer Nature, 2026, doi:10.1007/s00031-026-09958-y.
short: M.M. Elkner, Transformation Groups (2026).
corr_author: '1'
das_tickbox: '1'
date_created: 2026-03-23T15:10:43Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-07-22T07:37:35Z
day: '14'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00031-026-09958-y
external_id:
arxiv:
- '2411.16270'
fulldoi: https://doi.org/10.1007/s00031-026-09958-y
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00031-026-09958-y
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Transformation Groups
publication_identifier:
eissn:
- 1531-586X
issn:
- 1083-4362
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On involutions of minuscule Kirillov algebras induced by real structures
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
_id: '22694'
abstract:
- lang: eng
text: "We develop and employ techniques from equivariant algebraic K-theory and
related invariants\r\nin the context of geometric representation theory, in both
arithmetic and topological situations.\r\nWe showcase the use of such techniques
on the affine Grassmannian Gr, a space of fundamental\r\ninterest in the geometric
Langlands program.\r\n\r\nIt is a deep development of mathematics of the last
century that many concrete, yet combina-\r\ntorially complex algebraic problems
may be effectively studied through the lens of algebraic\r\ngeometry. The objects
of interest can be often realized as cohomological invariants of algebraic\r\nvarieties,
and good understanding of their geometry sheds light into the original questions.\r\nSuch
techniques have seen immense applications in the Langlands program, where they
go\r\nunder the label of geometric representation theory.\r\n\r\nOne source of
powerful invariants in algebraic geometry comes from algebraic K-theory,\r\nHochschild
homology, and their relatives. These localizing invariants contain large amount\r\nof
information, but are quite hard to compute. For this reason, their usage in geometric\r\nrepresentation
theory has been limited.\r\n\r\nThe aim of this thesis is to showcase how to control
such invariants in the situations of\r\ninterest and use them to obtain new insights.
We start by reinterpreting equivariant Hochschild\r\nhomology in terms of functions
on certain fixed-point schemes, which are of independent\r\ninterest. We compare
it to equivariant K-theory via the trace map. We give new computations\r\nand
comparisons of such invariants of affine Schubert varieties in Gr, including arithmetic\r\nsituations.
We show that they behave much better than expected.\r\n\r\nWe finally utilize
this circle of ideas in a purely topological setting. We describe the varying\r\nfixed
points of the extended torus action on the affine Grassmannian, and use it to
compute\r\nits equivariant topological K-theory ring. The answer is nontrivial
and verifies an outstanding\r\nconjecture in the subject.\r\n\r\nWe compare, partly
conjecturally, the resulting K-theory ring to the completed center of an\r\nintegral
even hybrid quantum group and its deformed quantum category O. This gives a\r\ngenuine
application of our computations in pure representation theory."
acknowledgement: "It was funded by a DOC Fellowship of the Austrian Academy of Sciences
entitled Arithmetic,\r\ngeometry, topology and representation theory arising from
the affine Grassmannian. It was\r\nfurther funded by the Austrian Science Fund FWF
10.55776/P35847, and an Erasmus+ staff\r\nmobility training. \r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Jakub
full_name: Löwit, Jakub
id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
last_name: Löwit
citation:
ama: Löwit J. Equivariant K-theory of affine Grassmannians in representation theory
and arithmetic. 2026. doi:10.15479/AT-ISTA-22694
apa: Löwit, J. (2026). Equivariant K-theory of affine Grassmannians in representation
theory and arithmetic. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-22694
chicago: Löwit, Jakub. “Equivariant K-Theory of Affine Grassmannians in Representation
Theory and Arithmetic.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-22694.
ieee: J. Löwit, “Equivariant K-theory of affine Grassmannians in representation
theory and arithmetic,” Institute of Science and Technology Austria, 2026.
ista: Löwit J. 2026. Equivariant K-theory of affine Grassmannians in representation
theory and arithmetic. Institute of Science and Technology Austria.
mla: Löwit, Jakub. Equivariant K-Theory of Affine Grassmannians in Representation
Theory and Arithmetic. Institute of Science and Technology Austria, 2026,
doi:10.15479/AT-ISTA-22694.
short: J. Löwit, Equivariant K-Theory of Affine Grassmannians in Representation
Theory and Arithmetic, Institute of Science and Technology Austria, 2026.
corr_author: '1'
date_created: 2026-08-12T14:05:36Z
date_published: 2026-08-05T00:00:00Z
date_updated: 2026-08-26T06:53:55Z
day: '05'
ddc:
- '510'
- '516'
- '512'
- '514'
- '513'
degree_awarded: PhD
department:
- _id: GradSch
- _id: TaHa
doi: 10.15479/AT-ISTA-22694
doi_confirm: '1'
file:
- access_level: open_access
checksum: 2d0be77791dc296621c6c0f76be9d0d7
content_type: application/pdf
creator: jloewit
date_created: 2026-08-14T11:42:31Z
date_updated: 2026-08-14T11:42:31Z
file_id: '22709'
file_name: 2026_Löwit_Jakub_Thesis.pdf
file_size: 1574709
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content_type: application/zip
creator: jloewit
date_created: 2026-08-14T11:42:42Z
date_updated: 2026-08-14T11:42:42Z
file_id: '22710'
file_name: 2026_Löwit_Jakub_Source_files.zip
file_size: 1085118
relation: source_file
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fulldoi: https://doi.org/10.15479/AT-ISTA-22694
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: '185'
project:
- _id: 901e2a43-16d5-11f0-9cad-9cead34748d6
grant_number: '27004'
name: Arithmetic, geometry, topology and representation theory arising from the
affine Grassmannian
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publisher_comment: "For open access purposes, the author has applied a CC BY public
copyright\r\nlicense to any author-accepted manuscript version arising from this
submission."
related_material:
record:
- id: '21751'
relation: part_of_dissertation
status: public
- id: '22693'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
title: Equivariant K-theory of affine Grassmannians in representation theory and arithmetic
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22693'
abstract:
- lang: eng
text: We study torus-equivariant algebraic K-theory of affine Schubert varieties
in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant
Hochschild homology of perfect complexes, which has a geometric description in
terms of global functions on certain fixed-point schemes. We prove that Fp-linearly,
this comparison is an isomorphism. Our approach is quite constructive, resulting
in new computations of these K-theory rings. We establish various structural results
for equivariant perfect algebraic K-theory on the way; we believe these are of
independent interest.
acknowledgement: "I would like to thank the following people for fruitful discussions,\r\nhelpful
sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt,
Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck,
Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil
Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further
like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin
a previous version.\r\nThis work was done during author’s PhD at the Institute of
Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the
Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847.
For open access\r\npurposes, the author has applied a CC BY public copyright license
to any author-accepted\r\nmanuscript version arising from this submission."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
full_name: Löwit, Jakub
id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
last_name: Löwit
citation:
ama: Löwit J. Equivariant K-theory, affine Grassmannian and perfection. Documenta
Mathematica. 2026. doi:10.4171/dm/1064
apa: Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection.
Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/1064
chicago: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.”
Documenta Mathematica. EMS Press, 2026. https://doi.org/10.4171/dm/1064.
ieee: J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” Documenta
Mathematica. EMS Press, 2026.
ista: Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta
Mathematica.
mla: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” Documenta
Mathematica, EMS Press, 2026, doi:10.4171/dm/1064.
short: J. Löwit, Documenta Mathematica (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-12T13:29:17Z
date_published: 2026-03-26T00:00:00Z
date_updated: 2026-08-26T06:53:54Z
day: '26'
ddc:
- '500'
department:
- _id: GradSch
- _id: TaHa
doi: 10.4171/dm/1064
external_id:
arxiv:
- '2409.18925'
fulldoi: https://doi.org/10.4171/dm/1064
has_accepted_license: '1'
keyword:
- equivariant algebraic K-theory
- perfection in positive characteristic
- affine Grassmannian
- affine Schubert varieties
- Dennis trace map
- equivariant Hochschild homology
- fixed-point schemes
- toric varieties
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/DM/1064
mathsc:
- '19E08'
- 19L47
- 20G44
- 14G17
- 19D55
- 14F43
- 14L30
- 14D24
- 14M25
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '22694'
relation: dissertation_contains
status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Equivariant K-theory, affine Grassmannian and perfection
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19071'
abstract:
- lang: eng
text: "An action of a complex reductive group G on a smooth projective variety X
is regular when all regular unipotent elements in G act with finitely many fixed
points. Then the complex G\r\n-equivariant cohomology ring of X is isomorphic
to the coordinate ring of a certain regular fixed point scheme. Examples include
partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties.
We also show that a more general version of the fixed point scheme allows a generalisation
to GKM spaces, such as toric varieties."
acknowledgement: 'The first author was supported by an FWF grant “Geometry of the
top of the nilpotent cone” number P 35847. The second author was supported by an
Austrian Academy of Sciences DOC Fellowship “Topology of open smooth varieties with
a torus action”. '
article_number: '1'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- first_name: Kamil P
full_name: Rychlewicz, Kamil P
id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
last_name: Rychlewicz
citation:
ama: Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point
scheme. Epijournal de Geometrie Algebrique. 2025;9. doi:10.46298/epiga.2025.12591
apa: Hausel, T., & Rychlewicz, K. P. (2025). Spectrum of equivariant cohomology
as a fixed point scheme. Epijournal de Geometrie Algebrique. EPI Sciences.
https://doi.org/10.46298/epiga.2025.12591
chicago: Hausel, Tamás, and Kamil P Rychlewicz. “Spectrum of Equivariant Cohomology
as a Fixed Point Scheme.” Epijournal de Geometrie Algebrique. EPI Sciences,
2025. https://doi.org/10.46298/epiga.2025.12591.
ieee: T. Hausel and K. P. Rychlewicz, “Spectrum of equivariant cohomology as a fixed
point scheme,” Epijournal de Geometrie Algebrique, vol. 9. EPI Sciences,
2025.
ista: Hausel T, Rychlewicz KP. 2025. Spectrum of equivariant cohomology as a fixed
point scheme. Epijournal de Geometrie Algebrique. 9, 1.
mla: Hausel, Tamás, and Kamil P. Rychlewicz. “Spectrum of Equivariant Cohomology
as a Fixed Point Scheme.” Epijournal de Geometrie Algebrique, vol. 9, 1,
EPI Sciences, 2025, doi:10.46298/epiga.2025.12591.
short: T. Hausel, K.P. Rychlewicz, Epijournal de Geometrie Algebrique 9 (2025).
corr_author: '1'
date_created: 2025-02-23T23:01:56Z
date_published: 2025-02-03T00:00:00Z
date_updated: 2025-04-15T06:31:58Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.46298/epiga.2025.12591
external_id:
arxiv:
- '2212.11836'
file:
- access_level: open_access
checksum: 3915c6f117461502f7103878460428df
content_type: application/pdf
creator: dernst
date_created: 2025-02-25T06:53:27Z
date_updated: 2025-02-25T06:53:27Z
file_id: '19085'
file_name: 2025_Epiga_Hausel.pdf
file_size: 3276395
relation: main_file
success: 1
file_date_updated: 2025-02-25T06:53:27Z
fulldoi: https://doi.org/10.46298/epiga.2025.12591
has_accepted_license: '1'
intvolume: ' 9'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
- _id: 34cd0f74-11ca-11ed-8bc3-bf0492a14a24
grant_number: '26525'
name: Topology of open smooth varieties with a torus action
publication: Epijournal de Geometrie Algebrique
publication_identifier:
eissn:
- 2491-6765
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
record:
- id: '17157'
relation: earlier_version
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title: Spectrum of equivariant cohomology as a fixed point scheme
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...
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_id: '19621'
abstract:
- lang: eng
text: In this paper we obtain a complete description of all indecomposable characters
(central positive-definite functions) of inductive limits of the symmetric groups
under block diagonal embedding. As a corollary we obtain the full classification
of the isomorphism classes of these inductive limits.
acknowledgement: The authors were partially supported by the “Long-term program of
support of the Ukrainian research teams at the Polish Academy of Sciences carried
out in collaboration with the U.S. National Academy of Sciences with the financial
support of external partners”. The second author was also supported by the Austrian
Science Fund (FWF) grant “Geometry of the tip of the global nilpotent cone” no.
10.55776/P35847
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nikolay
full_name: Nessonov, Nikolay
last_name: Nessonov
- first_name: Nhok T
full_name: Ngo, Nhok T
id: 28e53c8c-896a-11ed-bdf8-f809043ce2f0
last_name: Ngo
citation:
ama: Nessonov N, Ngo NT. Indecomposable characters of inductive limits of symmetric
groups. Representation Theory. 2025;29(8):256-288. doi:10.1090/ert/689
apa: Nessonov, N., & Ngo, N. T. (2025). Indecomposable characters of inductive
limits of symmetric groups. Representation Theory. American Mathematical
Society. https://doi.org/10.1090/ert/689
chicago: Nessonov, Nikolay, and Nhok T Ngo. “Indecomposable Characters of Inductive
Limits of Symmetric Groups.” Representation Theory. American Mathematical
Society, 2025. https://doi.org/10.1090/ert/689.
ieee: N. Nessonov and N. T. Ngo, “Indecomposable characters of inductive limits
of symmetric groups,” Representation Theory, vol. 29, no. 8. American Mathematical
Society, pp. 256–288, 2025.
ista: Nessonov N, Ngo NT. 2025. Indecomposable characters of inductive limits of
symmetric groups. Representation Theory. 29(8), 256–288.
mla: Nessonov, Nikolay, and Nhok T. Ngo. “Indecomposable Characters of Inductive
Limits of Symmetric Groups.” Representation Theory, vol. 29, no. 8, American
Mathematical Society, 2025, pp. 256–88, doi:10.1090/ert/689.
short: N. Nessonov, N.T. Ngo, Representation Theory 29 (2025) 256–288.
corr_author: '1'
date_created: 2025-04-24T08:48:05Z
date_published: 2025-04-10T00:00:00Z
date_updated: 2025-05-05T06:59:07Z
day: '10'
ddc:
- '510'
department:
- _id: GradSch
- _id: TaHa
doi: 10.1090/ert/689
external_id:
arxiv:
- '2206.01964'
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file_size: 424364
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success: 1
file_date_updated: 2025-05-05T06:57:49Z
fulldoi: https://doi.org/10.1090/ert/689
has_accepted_license: '1'
intvolume: ' 29'
issue: '8'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '04'
oa: 1
oa_version: Published Version
page: 256-288
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Representation Theory
publication_identifier:
issn:
- 1088-4165
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Indecomposable characters of inductive limits of symmetric groups
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2025'
...
---
APC_amount: 2742,92 EUR
OA_place: publisher
OA_type: hybrid
_id: '18108'
abstract:
- lang: eng
text: Here we announce the construction and properties of a big commutative subalgebra
of the Kirillov algebra attached to a finite dimensional irreducible representation
of a complex semisimple Lie group. They are commutative finite flat algebras over
the cohomology of the classifying space of the group. They are isomorphic with
the equivariant intersection cohomology of affine Schubert varieties, endowing
the latter with a new ring structure. Study of the finer aspects of the structure
of the big algebras will also furnish the stalks of the intersection cohomology
with ring structure, thus ringifying Lusztig’s q-weight multiplicity polynomials
i.e., certain affine Kazhdan–Lusztig polynomials.
acknowledgement: "We thank Nigel Hitchin for discussions and the joint projects this
paper has grown out from. We thank Vladyslav Zveryk for collaboration on Theorem
2.3 and on the corresponding Magma code which implements big algebras. We thank
Hiraku Nakajima for discussions and pointing out Theorem 3.1.2, a result generalizing
our original observation in the= = 0 case. Special thanks go to Leonid Rybnikov
for patiently explaining his works, in particular crucial to Theorem 2.1. We thank
Michel Brion, Michael Finkelberg, Oscar García-Prada, Jakub Löwit, Joel Kamnitzer,
Friedrich Knop, Michael McBreen, Anton Mellit, Takuro Mochizuki, Shon Ngô, Kamil
Rychlewicz, Shiyu Shen, Leslie Spencer, Balázs Szendr ˝ oi, András Szenes, and Oksana\r\nYakimova
for comments and discussions. Kamil Rychlewicz and Daniel Bedats helped with the
Mathematica files for the figures, and we used the SM_isospin Tikz package of Izaak
Neutelings for drawing the baryon multiplets. We thank the referees for many useful
comments. We acknowledge funding from FWF grant “Geometry of the tip of the global
nilpotent cone” no. P 35847."
article_number: e2319341121
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
citation:
ama: Hausel T. Commutative avatars of representations of semisimple Lie groups.
Proceedings of the National Academy of Sciences of the United States of America.
2024;121(38). doi:10.1073/pnas.2319341121
apa: Hausel, T. (2024). Commutative avatars of representations of semisimple Lie
groups. Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences. https://doi.org/10.1073/pnas.2319341121
chicago: Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie
Groups.” Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences, 2024. https://doi.org/10.1073/pnas.2319341121.
ieee: T. Hausel, “Commutative avatars of representations of semisimple Lie groups,”
Proceedings of the National Academy of Sciences of the United States of America,
vol. 121, no. 38. National Academy of Sciences, 2024.
ista: Hausel T. 2024. Commutative avatars of representations of semisimple Lie groups.
Proceedings of the National Academy of Sciences of the United States of America.
121(38), e2319341121.
mla: Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie Groups.”
Proceedings of the National Academy of Sciences of the United States of America,
vol. 121, no. 38, e2319341121, National Academy of Sciences, 2024, doi:10.1073/pnas.2319341121.
short: T. Hausel, Proceedings of the National Academy of Sciences of the United
States of America 121 (2024).
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: "There are no data underlying this work.\r\n"
date_created: 2024-09-22T22:01:41Z
date_published: 2024-09-17T00:00:00Z
date_updated: 2026-10-21T10:58:34Z
day: '17'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1073/pnas.2319341121
external_id:
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- '39259592'
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file_size: 3764695
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has_accepted_license: '1'
intvolume: ' 121'
issue: '38'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- relation: press_release
url: https://ista.ac.at/en/news/big-algebras-a-dictionary-of-abstract-math/
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supplementarymaterial: no
title: Commutative avatars of representations of semisimple Lie groups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 121
year: '2024'
...
---
_id: '15339'
abstract:
- lang: eng
text: We define even very stable Higgs bundles and study the Hitchin map restricted
to their upward flows. In the GLn case, we classify the type (1,…,1) examples,
and find that they are governed by a root system formed by the roots of even height.
We discuss how the spectrum of equivariant cohomology of real and quaternionic
Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin
map on even cominuscule upward flows. The even upward flows in question are the
same as upward flows in Higgs bundle moduli spaces for quasi-split inner real
forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.
acknowledgement: Most of the research for this paper was done when the first author
visited the second author's group at IST Austria as a summer intern in 2022. The
second author was supported by an FWF grant "Geometry of the top of the nilpotent
cone" number P35847.
article_number: '2441009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miguel
full_name: González, Miguel
last_name: González
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
citation:
ama: González M, Hausel T. Hitchin map on even very stable upward flows. International
Journal of Mathematics. 2024;35(09). doi:10.1142/S0129167X2441009X
apa: González, M., & Hausel, T. (2024). Hitchin map on even very stable upward
flows. International Journal of Mathematics. World Scientific Publishing.
https://doi.org/10.1142/S0129167X2441009X
chicago: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
Flows.” International Journal of Mathematics. World Scientific Publishing,
2024. https://doi.org/10.1142/S0129167X2441009X.
ieee: M. González and T. Hausel, “Hitchin map on even very stable upward flows,”
International Journal of Mathematics, vol. 35, no. 09. World Scientific
Publishing, 2024.
ista: González M, Hausel T. 2024. Hitchin map on even very stable upward flows.
International Journal of Mathematics. 35(09), 2441009.
mla: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
Flows.” International Journal of Mathematics, vol. 35, no. 09, 2441009,
World Scientific Publishing, 2024, doi:10.1142/S0129167X2441009X.
short: M. González, T. Hausel, International Journal of Mathematics 35 (2024).
das_tickbox: '0'
date_created: 2024-04-21T22:00:54Z
date_published: 2024-04-04T00:00:00Z
date_updated: 2026-10-21T10:57:37Z
day: '04'
department:
- _id: TaHa
doi: 10.1142/S0129167X2441009X
external_id:
arxiv:
- '2303.01404'
isi:
- '001251179200003'
fulldoi: https://doi.org/10.1142/S0129167X2441009X
intvolume: ' 35'
isi: 1
issue: '09'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2303.01404
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: International Journal of Mathematics
publication_identifier:
eissn:
- 1793-6519
issn:
- 0129-167X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Hitchin map on even very stable upward flows
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2024'
...