Real characters in nilpotent blocks

2023/01/31 by Sambale, Benjamin
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2301.13440

Abstract

We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius-Schur indicators of those characters can be computed for p=2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius-Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups.

Related

• Real blocks with dihedral defect groups revisited
• Real Subpairs and Frobenius-Schur Indicators of Characters in 2-Blocks
• Frobenius-Schur indicators of characters in blocks with cyclic defect
• Character tables and defect groups
• Real characters in blocks