Character theory at a torsion element

2025/04/20 by Nadimpalli, Santosh, Pattanayak, Santosha, Prasad, Dipendra
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.14684

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.

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