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arXiv · 1906.03055

DG-Enhanced Hecke and KLR Algebras

Ruslan Maksimau·Pedro Vaz
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Abstract

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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BibTeXRIS

Ruslan Maksimau, Pedro Vaz. 2019-06-07. DG-Enhanced Hecke and KLR Algebras. https://doi.org/10.3842/sigma.2023.095

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