Homological stability for Iwahori-Hecke algebras

2020/06/07 by Richard Hepworth, Hepworth, Richard · 1 citation
Mathematics · #16E40 (primary) #20F36 (secondary) #20J06 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2006.04252

openalex publication_date 2020/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Iwahori-Hecke algebras H_n of type A_n-1 satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley-Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.

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