English

Homological stability for Iwahori-Hecke algebras

Algebraic Topology 2022-08-04 v3 Group Theory Representation Theory

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.

Keywords

Cite

@article{arxiv.2006.04252,
  title  = {Homological stability for Iwahori-Hecke algebras},
  author = {Richard Hepworth},
  journal= {arXiv preprint arXiv:2006.04252},
  year   = {2022}
}

Comments

44 pages. Minor changes. To appear in the Journal of Topology