Real Characters in Nilpotent Blocks

authored by

Benjamin Sambale

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Vietnam Journal of Mathematics

Volume

52

Pages

421-433

No. of pages

13

ISSN

2305-221X

Publication date

04.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.2301.13440 (Access: Open)
https://doi.org/10.1007/s10013-023-00623-5 (Access: Open)