Gelfand-Graev characters of the finite unitary groups

2006/11/01 by Nathaniel Thiem, Thiem, Nathaniel, C. Ryan Vinroot +1 · 1 citation
Mathematics · #05E05 #20C33 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0611010

openalex publication_date 2006/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand-Graev characters of the finite unitary group from a combinatorial point of view. In particular, we give the values of Gelfand-Graev characters at arbitrary elements, recover the decomposition multiplicities of degenerate Gelfand-Graev characters in terms of tableau combinatorics, and conclude with some multiplicity consequences.

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