Frobenius-Schur indicators of characters in blocks with cyclic defect
Group Theory
2019-01-21 v1 Representation Theory
Abstract
Let be an odd prime and let be a -block of a finite group which has cyclic defect groups. We show that all exceptional characters in have the same Frobenius-Schur indicators. Moreover the common indicator can be computed, using the canonical character of . We also investigate the Frobenius-Schur indicators of the non-exceptional characters in . For a finite group which has cyclic Sylow -subgroups, we show that the number of irreducible characters with Frobenius-Schur indicator is greater than or equal to the number of conjugacy classes of weakly real -elements in .
Keywords
Cite
@article{arxiv.1901.06297,
title = {Frobenius-Schur indicators of characters in blocks with cyclic defect},
author = {John Murray},
journal= {arXiv preprint arXiv:1901.06297},
year = {2019}
}
Comments
17 pages