DG-Enhanced Hecke and KLR Algebras

We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion, DG-enhanced versions of affine Hecke algebras (degenerate or nondegenerate) are isomorphic to complet...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2023
Hauptverfasser: Maksimau, Ruslan, Vaz, Pedro
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2023
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212036
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:DG-Enhanced Hecke and KLR Algebras. Ruslan Maksimau and Pedro Vaz. SIGMA 19 (2023), 095, 24 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Maksimau, Ruslan
Vaz, Pedro
author_facet Maksimau, Ruslan
Vaz, Pedro
citation_txt DG-Enhanced Hecke and KLR Algebras. Ruslan Maksimau and Pedro Vaz. SIGMA 19 (2023), 095, 24 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion, DG-enhanced versions of affine Hecke algebras (degenerate or nondegenerate) are isomorphic to completed DG-enhanced versions of KLR algebras for suitably defined quivers. As a byproduct, we deduce that these DG-algebras have homologies concentrated in degree zero. These homologies are isomorphic respectively to the degenerate cyclotomic Hecke algebra and the cyclotomic Hecke algebra.
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language English
last_indexed 2026-03-14T21:24:54Z
publishDate 2023
publisher Інститут математики НАН України
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spelling Maksimau, Ruslan
Vaz, Pedro
2026-01-23T10:09:52Z
2023
DG-Enhanced Hecke and KLR Algebras. Ruslan Maksimau and Pedro Vaz. SIGMA 19 (2023), 095, 24 pages
1815-0659
2020 Mathematics Subject Classification: 20C08; 16E45
arXiv:1906.03055
https://nasplib.isofts.kiev.ua/handle/123456789/212036
https://doi.org/10.3842/SIGMA.2023.095
We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion, DG-enhanced versions of affine Hecke algebras (degenerate or nondegenerate) are isomorphic to completed DG-enhanced versions of KLR algebras for suitably defined quivers. As a byproduct, we deduce that these DG-algebras have homologies concentrated in degree zero. These homologies are isomorphic respectively to the degenerate cyclotomic Hecke algebra and the cyclotomic Hecke algebra.
We thank Jonathan Grant for useful discussions and the anonymous referees for the careful reading of our document. The Fonds de la Recherche Scientifique supported PV– FNRS under Grant No. MIS-F.4536.19.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
DG-Enhanced Hecke and KLR Algebras
Article
published earlier
spellingShingle DG-Enhanced Hecke and KLR Algebras
Maksimau, Ruslan
Vaz, Pedro
title DG-Enhanced Hecke and KLR Algebras
title_full DG-Enhanced Hecke and KLR Algebras
title_fullStr DG-Enhanced Hecke and KLR Algebras
title_full_unstemmed DG-Enhanced Hecke and KLR Algebras
title_short DG-Enhanced Hecke and KLR Algebras
title_sort dg-enhanced hecke and klr algebras
url https://nasplib.isofts.kiev.ua/handle/123456789/212036
work_keys_str_mv AT maksimauruslan dgenhancedheckeandklralgebras
AT vazpedro dgenhancedheckeandklralgebras