Zeros of $S$-characters
Group Theory
2026-05-18 v3 Representation Theory
Abstract
The concept of -characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial -character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. We present examples that this does not generalise to -characters, thereby answering a question posed by J-P. Serre.
Cite
@article{arxiv.2408.16785,
title = {Zeros of $S$-characters},
author = {Thomas Breuer and Michael Joswig and Gunter Malle},
journal= {arXiv preprint arXiv:2408.16785},
year = {2026}
}
Comments
extended the computations, made relation to polytope theory, added two new authors