Brauer's 14th Problem and Dyson's Tenfold Way
Group Theory
2025-07-01 v3 Representation Theory
Abstract
We consider Brauer's 14th Problem in the context of "Real" structures on finite groups and their antilinear representations. The problem is to count the number of characters of each different type using "group theory". While Brauer's original problem deals only with three types (real, complex and quaternionic), here we consider the ten types coming from Dyson's tenfold way.
Keywords
Cite
@article{arxiv.2503.10590,
title = {Brauer's 14th Problem and Dyson's Tenfold Way},
author = {Dmitriy Rumynin and James Taylor},
journal= {arXiv preprint arXiv:2503.10590},
year = {2025}
}
Comments
Version 2: the problem posed in Version 1 is solved. Version 3: minor changes, in line with the journal version