On Jordan Decomposition of Characters for SU(n,q)

2011/12/28 by Marc Cabanes, Cabanes, Marc
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1112.6035

18 pages

arxiv created 2011/12/28 · arxiv updated 2011/12/30

Abstract

As shown by Bonnafé, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the same kind of result in the case of finite special unitary groups. The proof leads to a mild adaptation of Bonnafé's methods expounded in [B99]. The outcome is a Jordan decomposition of characters compatible with Lusztig's twisted induction.

Related

• Quadratic unipotent blocks in general linear, unitary and symplectic groups
• Harish-Chandra Induction and Jordan Decomposition of Characters
• Jordan correspondence and block distribution of characters
• Further results for classical and universal characters twisted by roots of unity
• Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer