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 |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| 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| _version_ | 1862633845994553344 |
|---|---|
| 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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| first_indexed | 2026-03-14T21:24:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212036 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T21:24:54Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |