DG-enhanced Hecke and KLR algebras
(2023) SIGMA — Vol. 19 (2023)
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- Abstract
- We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine q-Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion DG-enhanced versions of Hecke algebras 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 q-Hecke algebra.
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Citations
Dos Santos Santana Forte Vaz, P., & Maksimau, R. (2023). DG-enhanced Hecke and KLR algebras. SIGMA, 19. https://doi.org/10.3842/SIGMA.2023.095 (Original work published 2023)