Character theory at a torsion element
Representation Theory
2025-04-22 v1
Abstract
The paper relates character value of an irreducible representation of a compact connected Lie group at certain elements of finite order with the dimension of a representation on another group, up to some precise constants, which all have significance. An important input is to analyse torsion elements of order d in an adjoint group with minimal dimensional centraliser, and to prove that in most cases when d divides the Coxeter number of G, this gives rise to a unique conjugacy class.
Cite
@article{arxiv.2504.14684,
title = {Character theory at a torsion element},
author = {Santosh Nadimpalli and Santosha Pattanayak and Dipendra Prasad},
journal= {arXiv preprint arXiv:2504.14684},
year = {2025}
}