English

Frobenius-Schur indicators of characters in blocks with cyclic defect

Group Theory 2019-01-21 v1 Representation Theory

Abstract

Let pp be an odd prime and let BB be a pp-block of a finite group which has cyclic defect groups. We show that all exceptional characters in BB have the same Frobenius-Schur indicators. Moreover the common indicator can be computed, using the canonical character of BB. We also investigate the Frobenius-Schur indicators of the non-exceptional characters in BB. For a finite group which has cyclic Sylow pp-subgroups, we show that the number of irreducible characters with Frobenius-Schur indicator 1-1 is greater than or equal to the number of conjugacy classes of weakly real pp-elements in GG.

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}
}

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17 pages