Character values at elements of order 2

2024/12/23 by Chayan Karmakar, Karmakar, Chayan
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2412.17324

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 G₂ 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.

Related

• The values of unipotent characters at unipotent elements for groups of type E₈ and ² E₆
• Character Levels and Character Bounds. II
• On the computation of character values for finite Chevalley groups of exceptional type
• Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2
• Short character values on large conjugacy classes