Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras

2020/05/06 by Bowman, Chris, Cox, Anton, Hazi, Amit · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2005.02825

Abstract

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these algebras (including as examples the symmetric groups and generalised blob algebras) are tautologically equal to the associated p-Kazhdan-Lusztig polynomials, provided that the characteristic is greater than the Coxeter number. We hence give an elementary and more explicit proof of the main theorem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic Hecke algebras, thus solving Libedinsky-Plaza's categorical blob conjecture.

Cited by

• Morita equivalences between cyclotomic KLR algebras in types \mathttC_∞ and \mathttA_∞

Related

• Path combinatorics and light leaves for quiver Hecke algebras
• Presenting Hecke endomorphism algebras by Hasse quivers with relations
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach
• Quiver Heisenberg algebras: a cubic analogue of preprojective algebras
• Stratifying Hecke endomorphism algebras using exact categories