Details
| Original language | English |
|---|---|
| Pages (from-to) | 421-433 |
| Number of pages | 13 |
| Journal | Vietnam Journal of Mathematics |
| Volume | 52 |
| Issue number | 2 |
| Early online date | 8 May 2023 |
| Publication status | Published - Apr 2024 |
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
ASJC Scopus subject areas
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In: Vietnam Journal of Mathematics, Vol. 52, No. 2, 04.2024, p. 421-433.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Real Characters in Nilpotent Blocks
AU - Sambale, Benjamin
N1 - Funding Information: The work is supported by the German Research Foundation (SA 2864/3-1 and SA 2864/4-1).
PY - 2024/4
Y1 - 2024/4
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 - http://www.scopus.com/inward/record.url?scp=85158103368&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2301.13440
DO - 10.48550/arXiv.2301.13440
M3 - Article
AN - SCOPUS:85158103368
VL - 52
SP - 421
EP - 433
JO - Vietnam Journal of Mathematics
JF - Vietnam Journal of Mathematics
SN - 2305-221X
IS - 2
ER -