Rational representations and permutation representations of finite groups
Representation Theory
2016-01-29 v2 Group Theory
Abstract
We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.
Cite
@article{arxiv.1405.6616,
title = {Rational representations and permutation representations of finite groups},
author = {Alex Bartel and Tim Dokchitser},
journal= {arXiv preprint arXiv:1405.6616},
year = {2016}
}
Comments
16 pages; minor improvements and corrections. To appear in Math. Ann