DG-Enhanced Hecke and KLR Algebras
Representation Theory
2023-11-23 v3
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.
Cite
@article{arxiv.1906.03055,
title = {DG-Enhanced Hecke and KLR Algebras},
author = {Ruslan Maksimau and Pedro Vaz},
journal= {arXiv preprint arXiv:1906.03055},
year = {2023}
}