Bounding Harish-Chandra series
Representation Theory
2017-01-06 v1 Group Theory
Abstract
We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As a first application we show the irreducibility of the smallest unipotent character in any Harish-Chandra series. Secondly, we determine a unitriangular approximation to part of the unipotent decomposition matrix of finite orthogonal groups and prove a gap result on certain Brauer character degrees.
Keywords
Cite
@article{arxiv.1701.01260,
title = {Bounding Harish-Chandra series},
author = {Olivier Dudas and Gunter Malle},
journal= {arXiv preprint arXiv:1701.01260},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1611.07373