---
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'
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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
OA_type: hybrid
PlanS_conform: '1'
_id: '17437'
abstract:
- lang: eng
text: We prove that the zero-fiber of the moment map of a totally negative quiver
has rational singularities. Our proof consists in generalizing dimension bounds
on jet spaces of this fiber, which were introduced by Budur. We also transfer
the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau
categories, based on recent work of Davison. This has interesting arithmetic applications
on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories.
First, we generalize results of Wyss on the asymptotic behaviour of counts of
jets of quiver moment maps over finite fields. Moreover, we interpret the limit
of counts of jets on a given moduli space as its p-adic volume under a canonical
measure analogous to the measure built by Carocci, Orecchia and Wyss on certain
moduli spaces of coherent sheaves.
acknowledgement: "I would like to warmly thank Dimitri Wyss for his guidance and supervision
and Nero Budur for helpful discussions and answering all my questions on his previous
works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart
and Olivier Schiffmann for helpful remarks and discussions during the writing of
this paper. Finally, I would like to thank the anonymous referees for their careful
reading and suggesting improvements in the exposition.\r\nOpen access funding provided
by Institute of Science and Technology (IST Austria). This work was supported by
the Swiss National Science Foundation [No. 196960]. This project has also received
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant Agreement No. 101034413."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Tanguy
full_name: Vernet, Tanguy
id: 19f1e3bf-c59a-11ee-a1af-ed269948817b
last_name: Vernet
citation:
ama: Vernet T. Rational singularities for moment maps of totally negative quivers.
Transformation Groups. 2026;31:1047-1083. doi:10.1007/s00031-024-09873-0
apa: Vernet, T. (2026). Rational singularities for moment maps of totally negative
quivers. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-024-09873-0
chicago: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
Quivers.” Transformation Groups. Springer Nature, 2026. https://doi.org/10.1007/s00031-024-09873-0.
ieee: T. Vernet, “Rational singularities for moment maps of totally negative quivers,”
Transformation Groups, vol. 31. Springer Nature, pp. 1047–1083, 2026.
ista: Vernet T. 2026. Rational singularities for moment maps of totally negative
quivers. Transformation Groups. 31, 1047–1083.
mla: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
Quivers.” Transformation Groups, vol. 31, Springer Nature, 2026, pp. 1047–83,
doi:10.1007/s00031-024-09873-0.
short: T. Vernet, Transformation Groups 31 (2026) 1047–1083.
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: Not applicable.
date_created: 2024-08-18T22:01:04Z
date_published: 2026-03-01T00:00:00Z
date_updated: 2026-07-23T05:51:07Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00031-024-09873-0
ec_funded: 1
external_id:
isi:
- '001287455300001'
file:
- access_level: open_access
checksum: 8985b4154b730284d3412ddc9e55d965
content_type: application/pdf
creator: dernst
date_created: 2026-07-23T05:50:09Z
date_updated: 2026-07-23T05:50:09Z
file_id: '22385'
file_name: 2026_TransformationGroups_Vernet.pdf
file_size: 912029
relation: main_file
success: 1
file_date_updated: 2026-07-23T05:50:09Z
has_accepted_license: '1'
intvolume: ' 31'
isi: 1
language:
- iso: eng
mathsc:
- 14B05
- 14D23
- 14G20
- 16G20
month: '03'
oa: 1
oa_version: Published Version
page: 1047-1083
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Transformation Groups
publication_identifier:
eissn:
- 1531-586X
issn:
- 1083-4362
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Rational singularities for moment maps of totally negative quivers
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: 31
year: '2026'
...
---
_id: '7940'
abstract:
- lang: eng
text: We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody
Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter
is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras.
As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this
class of affine Yangians. Another independent proof of the PBW theorem is given
recently by Guay, Regelskis, and Wendlandt [GRW18].
acknowledgement: Gufang Zhao is affiliated to IST Austria, Hausel group until July
of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli
spaces No. 320593 of the European Research Council.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yaping
full_name: Yang, Yaping
id: 360D8648-F248-11E8-B48F-1D18A9856A87
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The PBW theorem for affine Yangians. Transformation Groups.
2020;25:1371-1385. doi:10.1007/s00031-020-09572-6
apa: Yang, Y., & Zhao, G. (2020). The PBW theorem for affine Yangians. Transformation
Groups. Springer Nature. https://doi.org/10.1007/s00031-020-09572-6
chicago: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups. Springer Nature, 2020. https://doi.org/10.1007/s00031-020-09572-6.
ieee: Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” Transformation
Groups, vol. 25. Springer Nature, pp. 1371–1385, 2020.
ista: Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation
Groups. 25, 1371–1385.
mla: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:10.1007/s00031-020-09572-6.
short: Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.
date_created: 2020-06-07T22:00:55Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2025-07-10T11:54:50Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00031-020-09572-6
ec_funded: 1
external_id:
arxiv:
- '1804.04375'
isi:
- '000534874300003'
intvolume: ' 25'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.04375
month: '12'
oa: 1
oa_version: Preprint
page: 1371-1385
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Transformation Groups
publication_identifier:
eissn:
- 1531-586X
issn:
- 1083-4362
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The PBW theorem for affine Yangians
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...