Character values at elements of order 2

期刊论文
发表日期：

2025年11月27日

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Chayan Karmakar

摘要

In this paper, we compute the character values of irreducible, integrable highest weight representations for classical groups of types $ A_n $ $A_{n}$ , $ B_n $ $B_{n}$ , $ C_n $ $C_{n}$ , $ D_n $ $D_{n}$ and the exceptional group $G_2$ $G_{2}$ at all conjugacy classes of elements of order 2. We prove that these character values, if nonzero, can be expressed either as a product involving the dimensions of two irreducible, integrable highest weight representations from classical subgroups, up to a constant factor, or as an alternating sum of products of the dimensions of two irreducible, integrable highest weight representations from the classical subgroups, up to a constant factor.