Real Characters in Nilpotent Blocks

Benjamin Sambale

doi:10.48550/arXiv.2301.13440

Real Characters in Nilpotent Blocks

Benjamin Sambale^*

^*Corresponding author for this work

Institute of Algebra, Number Theory and Discrete Mathematics

Research output: Contribution to journal › Article › Research › peer review

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.

Original language	English
Pages (from-to)	421-433
Number of pages	13
Journal	Vietnam Journal of Mathematics
Volume	52
Issue number	2
E-pub ahead of print	8 May 2023
DOIs	https://doi.org/10.48550/arXiv.2301.13440 https://doi.org/10.1007/s10013-023-00623-5
Publication status	Published - Apr 2024

Keywords

20C15
20C20
Frobenius–Schur indicators
Nilpotent blocks
Real characters

ASJC Scopus subject areas

General Mathematics

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10.48550/arXiv.2301.13440Licence: Arxiv nonexclusive-distrib 1.0
10.1007/s10013-023-00623-5Licence: CC BY 4.0

Cite this

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title = "Real Characters in Nilpotent Blocks",

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.",

keywords = "20C15, 20C20, Frobenius–Schur indicators, Nilpotent blocks, Real characters",

author = "Benjamin Sambale",

note = "Funding Information: The work is supported by the German Research Foundation (SA 2864/3-1 and SA 2864/4-1). ",

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N2 - 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.

AB - 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.

KW - 20C15

KW - 20C20

KW - Frobenius–Schur indicators

KW - Nilpotent blocks

KW - Real characters

UR - https://www.scopus.com/pages/publications/85158103368

U2 - 10.48550/arXiv.2301.13440

DO - 10.48550/arXiv.2301.13440

M3 - Article

AN - SCOPUS:85158103368

SN - 2305-221X

VL - 52

SP - 421

EP - 433

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 2

ER -

Real Characters in Nilpotent Blocks

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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