The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups E₇(q)

2003/06/18 by Meinolf Geck, Geck, Meinolf
Mathematics · #20C15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C15

paper · pdf · doi:10.48550/arxiv.math/0306268

12 pages

arxiv created 2003/06/18 · openalex publication_date 2003/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the two cuspidal unipotent characters of a finite Chevalley group E₇(q) have Schur index~2, provided that q is an even power of a (sufficiently large) prime number p such that p≡ 1 \bmod 4. The proof uses a refinement of Kawanaka's generalized Gelfand--Graev representations and some explicit computations with the \sf CHEVIE computer algebra system.

Related

• On the Schur indices of cuspidal unipotent characters
• The character table of the finite Chevalley group F₄(q) for q a power of~2
• On the computation of character values for finite Chevalley groups of exceptional type
• On the values of unipotent characters of finite Chevalley groups of type E₆ in characteristic 3
• On the values of unipotent characters of finite Chevalley groups of type\n E₇ in characteristic 2