Harish-Chandra theories, Ennola $d$-ality and Rouquier blocks for spetses

Gunter Malle

Harish-Chandra theories, Ennola $d$-ality and Rouquier blocks for spetses

Representation Theory 2026-07-01 v1

Authors: Gunter Malle

Abstract

It has been shown that the theory of unipotent characters of finite reductive groups admits a generalisation to objects whose Weyl group is a spetsial complex reflection group, called spetses. In this paper we prove several natural properties satisfied by the unipotent characters of spetses, in particular the validity of all Harish-Chandra theories as well as the existence of Ennola $d$ -alities for all integers $d$ , Alvis--Curtis duality, and compatibility with Rouquier blocks of relative Hecke algebras.

Keywords

unipotent characters spetses Harish-Chandra theory Ennola duality Alvis-Curtis duality Rouquier blocks

Cite

@article{arxiv.2607.00515,
  title  = {Harish-Chandra theories, Ennola $d$-ality and Rouquier blocks for spetses},
  author = {Gunter Malle},
  journal= {arXiv preprint arXiv:2607.00515},
  year   = {2026}
}