Character values at elements of order 2

TL;DR

This paper computes character values at elements of order 2 for highest weight representations of classical and exceptional groups, revealing formulas involving subgroup representations and constants.

Contribution

It provides explicit formulas for character values at order 2 elements for a wide class of groups, including classical and G_2, with novel expressions involving subgroup representations.

Findings

Character values are expressed as products or alternating sums involving subgroup dimensions.

Formulas apply to all conjugacy classes of order 2 in the considered groups.

Results extend understanding of character theory for classical and exceptional groups.

Abstract

In this paper we compute the character values of highest weight representations for classical groups of types A_n, B_n, C_n, D_n and the Exceptional group G_2 at all conjugacy classes of order 2. We prove that these character values, if nonzero, can be expressed either as a product involving the dimensions of two highest weight representations from classical subgroups, along with an additional constant term, or as an alternating sum of products of the dimensions of two highest weight representations from the classical subgroups, also accompanied by an extra constant term.