Homological stability for Iwahori-hecke algebras

Richard Hepworth

doi:10.1112/topo.12262

Homological stability for Iwahori-hecke algebras

Richard Hepworth

Mathematical Science

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the Iwahori-Hecke algebras Hn of type An−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.

Original language	English
Pages (from-to)	2174-2215
Journal	Journal of Topology
Volume	15
Issue number	4
Early online date	8 Oct 2022
DOIs	https://doi.org/10.1112/topo.12262
Publication status	Published - Dec 2022

Access to Document

10.1112/topo.12262Licence: CC BY

Hepworth_JT_Homological_Stability_For_AAM
This is the accepted version of the following article: FULL CITE, which has been published in final form at [Link to final article]
Accepted author manuscript, 465 KBLicence: Other
Hepworth_JoT_Homological_Stability_For_VOR
© 2022 The Authors. Journal of Topology is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Final published version, 322 KBLicence: CC BY

Cite this

@article{8990d4d6e4594aba899549d1307d1561,

title = "Homological stability for Iwahori-hecke algebras",

abstract = "We show that the Iwahori-Hecke algebras Hn of type An−1 satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka{\textquoteright}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.",

author = "Richard Hepworth",

note = "ACKNOWLEDGEMENT I would like to thank the anonymous referee, whose comments helped to significantly improve the readability of the paper.",

year = "2022",

month = dec,

doi = "10.1112/topo.12262",

language = "English",

volume = "15",

pages = "2174--2215",

journal = "Journal of Topology",

issn = "1753-8416",

publisher = "John Wiley and Sons Ltd",

number = "4",

}

TY - JOUR

T1 - Homological stability for Iwahori-hecke algebras

AU - Hepworth, Richard

N1 - ACKNOWLEDGEMENT I would like to thank the anonymous referee, whose comments helped to significantly improve the readability of the paper.

PY - 2022/12

Y1 - 2022/12

N2 - We show that the Iwahori-Hecke algebras Hn of type An−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.

AB - We show that the Iwahori-Hecke algebras Hn of type An−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.

U2 - 10.1112/topo.12262

DO - 10.1112/topo.12262

M3 - Article

VL - 15

SP - 2174

EP - 2215

JO - Journal of Topology

JF - Journal of Topology

SN - 1753-8416

IS - 4

ER -

Homological stability for Iwahori-hecke algebras

Abstract

Access to Document

Fingerprint

Cite this