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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Zusammenfassung: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.
ISSN:1815-0659