---
OA_place: publisher
OA_type: hybrid
_id: '18154'
abstract:
- lang: eng
  text: 'In 1976, Deligne and Lusztig realized the representation theory of finite
    groups of Lie type inside étale cohomology of certain algebraic varieties. Recently,
    a p-adic version of this theory started to emerge: there are p-adic Deligne–Lusztig
    spaces, whose cohomology encodes representation theoretic information for p-adic
    groups – for instance, it partially realizes the local Langlands correspondence
    with characteristic zero coefficients. However, the parallel case of coefficients
    of positive characteristic  ℓ≠p has not been inspected so far. The purpose of
    this article is to initiate such an inspection. In particular, we relate cohomology
    of certain p-adic Deligne–Lusztig spaces to Vignéras''s modular local Langlands
    correspondence for GLn.'
article_processing_charge: Yes (via OA deal)
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. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn.
    <i>Journal of Algebra</i>. 2025;663(2):81-118. doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">10.1016/j.jalgebra.2024.08.033</a>
  apa: Löwit, J. (2025). On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties
    for GLn. <i>Journal of Algebra</i>. Elsevier. <a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">https://doi.org/10.1016/j.jalgebra.2024.08.033</a>
  chicago: Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties
    for GLn.” <i>Journal of Algebra</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">https://doi.org/10.1016/j.jalgebra.2024.08.033</a>.
  ieee: J. Löwit, “On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for
    GLn,” <i>Journal of Algebra</i>, vol. 663, no. 2. Elsevier, pp. 81–118, 2025.
  ista: Löwit J. 2025. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties
    for GLn. Journal of Algebra. 663(2), 81–118.
  mla: Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties for
    GLn.” <i>Journal of Algebra</i>, vol. 663, no. 2, Elsevier, 2025, pp. 81–118,
    doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">10.1016/j.jalgebra.2024.08.033</a>.
  short: J. Löwit, Journal of Algebra 663 (2025) 81–118.
corr_author: '1'
date_created: 2024-09-29T22:01:37Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-02-27T12:32:40Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1016/j.jalgebra.2024.08.033
external_id:
  arxiv:
  - '2404.11176'
  isi:
  - '001325207800001'
file:
- access_level: open_access
  checksum: eb240e93c178e48429ad918c9058f1fe
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  creator: dernst
  date_created: 2025-01-13T08:57:57Z
  date_updated: 2025-01-13T08:57:57Z
  file_id: '18830'
  file_name: 2024_JourAlgebra_Loewit.pdf
  file_size: 731175
  relation: main_file
  success: 1
file_date_updated: 2025-01-13T08:57:57Z
has_accepted_license: '1'
intvolume: '       663'
isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 81-118
publication: Journal of Algebra
publication_identifier:
  eissn:
  - 1090-266X
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn
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: 663
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18617'
abstract:
- lang: eng
  text: "Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination
    of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation
    of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1
    is not only sufficient, but also necessary for uniqueness of the separation. Moreover,
    we describe the structure of non-uniqueness of the separation in the boundary
    cases when n=2k−2 and n=2k−3.\r\nFormally, we study the kernel of a multiplication
    map ϕ carrying out separation of variables. We devise a general algorithmic procedure
    for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full
    non-stable range n<2k−1, we give formulas for highest weights of generators of
    the kernel as well as formulas for its Hilbert series. Using the developed methods,
    we obtain a list of highest weight vectors generating Ker ϕ."
acknowledgement: The author is sincerely grateful for guidance, advice and valuable
  feedback from Roman Lávička.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Daniel
  full_name: Beďatš, Daniel
  id: 78ea3cc9-31e7-11ee-aa02-a6169bbfe1f1
  last_name: Beďatš
  orcid: 0009-0004-1828-0044
citation:
  ama: Beďatš D. Separation of variables for scalar-valued polynomials in the non-stable
    range. <i>Journal of Algebra</i>. 2024;651:281-304. doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.04.013">10.1016/j.jalgebra.2024.04.013</a>
  apa: Beďatš, D. (2024). Separation of variables for scalar-valued polynomials in
    the non-stable range. <i>Journal of Algebra</i>. Elsevier. <a href="https://doi.org/10.1016/j.jalgebra.2024.04.013">https://doi.org/10.1016/j.jalgebra.2024.04.013</a>
  chicago: Beďatš, Daniel. “Separation of Variables for Scalar-Valued Polynomials
    in the Non-Stable Range.” <i>Journal of Algebra</i>. Elsevier, 2024. <a href="https://doi.org/10.1016/j.jalgebra.2024.04.013">https://doi.org/10.1016/j.jalgebra.2024.04.013</a>.
  ieee: D. Beďatš, “Separation of variables for scalar-valued polynomials in the non-stable
    range,” <i>Journal of Algebra</i>, vol. 651. Elsevier, pp. 281–304, 2024.
  ista: Beďatš D. 2024. Separation of variables for scalar-valued polynomials in the
    non-stable range. Journal of Algebra. 651, 281–304.
  mla: Beďatš, Daniel. “Separation of Variables for Scalar-Valued Polynomials in the
    Non-Stable Range.” <i>Journal of Algebra</i>, vol. 651, Elsevier, 2024, pp. 281–304,
    doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.04.013">10.1016/j.jalgebra.2024.04.013</a>.
  short: D. Beďatš, Journal of Algebra 651 (2024) 281–304.
corr_author: '1'
date_created: 2024-12-04T07:58:45Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T14:57:00Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1016/j.jalgebra.2024.04.013
external_id:
  arxiv:
  - '2309.11154'
  isi:
  - '001232775600001'
file:
- access_level: open_access
  checksum: 7b01c89128ba16d5334dfab389a03878
  content_type: application/pdf
  creator: dernst
  date_created: 2024-12-09T13:56:26Z
  date_updated: 2024-12-09T13:56:26Z
  file_id: '18638'
  file_name: 2024_JourAlgebra_Bedats.pdf
  file_size: 486969
  relation: main_file
  success: 1
file_date_updated: 2024-12-09T13:56:26Z
has_accepted_license: '1'
intvolume: '       651'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 281-304
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Separation of variables for scalar-valued polynomials in the non-stable range
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: 651
year: '2024'
...
---
_id: '11545'
abstract:
- lang: eng
  text: "We classify contravariant pairings between standard Whittaker modules and
    Verma modules over a complex semisimple Lie algebra. These contravariant pairings
    are useful in extending several classical techniques for category O to the Miličić–Soergel
    category N . We introduce a class of costandard modules which generalize dual
    Verma modules, and describe canonical maps from standard to costandard modules
    in terms of contravariant pairings.\r\nWe show that costandard modules have unique
    irreducible submodules and share the same composition factors as the corresponding
    standard Whittaker modules. We show that costandard modules give an algebraic
    characterization of the global sections of costandard twisted Harish-Chandra sheaves
    on the associated flag variety, which are defined using holonomic duality of D-modules.
    We prove that with these costandard modules, blocks of category\r\nN have the
    structure of highest weight categories and we establish a BGG reciprocity theorem
    for N ."
acknowledgement: We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting
  discussions. The first author acknowledges the support of the European Union's Horizon
  2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
  No. 754411. The second author is supported by the National Science Foundation Award
  No. 1803059 and the Australian Research Council grant DP170101579.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Adam
  full_name: Brown, Adam
  id: 70B7FDF6-608D-11E9-9333-8535E6697425
  last_name: Brown
- first_name: Anna
  full_name: Romanov, Anna
  last_name: Romanov
citation:
  ama: Brown A, Romanov A. Contravariant pairings between standard Whittaker modules
    and Verma modules. <i>Journal of Algebra</i>. 2022;609(11):145-179. doi:<a href="https://doi.org/10.1016/j.jalgebra.2022.06.017">10.1016/j.jalgebra.2022.06.017</a>
  apa: Brown, A., &#38; Romanov, A. (2022). Contravariant pairings between standard
    Whittaker modules and Verma modules. <i>Journal of Algebra</i>. Elsevier. <a href="https://doi.org/10.1016/j.jalgebra.2022.06.017">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>
  chicago: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard
    Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>. Elsevier, 2022.
    <a href="https://doi.org/10.1016/j.jalgebra.2022.06.017">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>.
  ieee: A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker
    modules and Verma modules,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier,
    pp. 145–179, 2022.
  ista: Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker
    modules and Verma modules. Journal of Algebra. 609(11), 145–179.
  mla: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker
    Modules and Verma Modules.” <i>Journal of Algebra</i>, vol. 609, no. 11, Elsevier,
    2022, pp. 145–79, doi:<a href="https://doi.org/10.1016/j.jalgebra.2022.06.017">10.1016/j.jalgebra.2022.06.017</a>.
  short: A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.
corr_author: '1'
date_created: 2022-07-08T11:40:07Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2025-04-14T07:43:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2022.06.017
ec_funded: 1
external_id:
  isi:
  - '000861841100004'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2023-02-02T07:32:48Z
  date_updated: 2023-02-02T07:32:48Z
  file_id: '12473'
  file_name: 2022_JournalAlgebra_Brown.pdf
  file_size: 582962
  relation: main_file
  success: 1
file_date_updated: 2023-02-02T07:32:48Z
has_accepted_license: '1'
intvolume: '       609'
isi: 1
issue: '11'
keyword:
- Algebra and Number Theory
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 145-179
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Contravariant pairings between standard Whittaker modules and Verma modules
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 609
year: '2022'
...
---
_id: '6828'
abstract:
- lang: eng
  text: In this paper we construct a family of exact functors from the category of
    Whittaker modules of the simple complex Lie algebra of type  to the category of
    finite-dimensional modules of the graded affine Hecke algebra of type . Using
    results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors
    map standard modules to standard modules (or zero) and simple modules to simple
    modules (or zero). Moreover, we show that each simple module of the graded affine
    Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker
    category contains the BGG category  as a full subcategory, our results generalize
    results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between
    finite-dimensional representations of  and representations of the symmetric group
    .
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adam
  full_name: Brown, Adam
  id: 70B7FDF6-608D-11E9-9333-8535E6697425
  last_name: Brown
citation:
  ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>.
    2019;538:261-289. doi:<a href="https://doi.org/10.1016/j.jalgebra.2019.07.027">10.1016/j.jalgebra.2019.07.027</a>
  apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. <i>Journal
    of Algebra</i>. Elsevier. <a href="https://doi.org/10.1016/j.jalgebra.2019.07.027">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>
  chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal
    of Algebra</i>. Elsevier, 2019. <a href="https://doi.org/10.1016/j.jalgebra.2019.07.027">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>.
  ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” <i>Journal of Algebra</i>,
    vol. 538. Elsevier, pp. 261–289, 2019.
  ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
    538, 261–289.
  mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of
    Algebra</i>, vol. 538, Elsevier, 2019, pp. 261–89, doi:<a href="https://doi.org/10.1016/j.jalgebra.2019.07.027">10.1016/j.jalgebra.2019.07.027</a>.
  short: A. Brown, Journal of Algebra 538 (2019) 261–289.
date_created: 2019-08-22T07:54:13Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2023-08-29T07:11:47Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2019.07.027
external_id:
  arxiv:
  - '1805.04676'
  isi:
  - '000487176300011'
intvolume: '       538'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1805.04676
month: '11'
oa: 1
oa_version: Preprint
page: 261-289
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Arakawa-Suzuki functors for Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 538
year: '2019'
...