Real representations of finite symplectic groups over fields of characteristic two

C. Ryan Vinroot

Real representations of finite symplectic groups over fields of characteristic two

Representation Theory 2017-08-25 v1 Combinatorics Group Theory

Authors: C. Ryan Vinroot

Abstract

We prove that when $q$ is a power of $2$ , every complex irreducible representation of $\mathrm{Sp}(2n, \mathbb{F}_q)$ may be defined over the real numbers, that is, all Frobenius-Schur indicators are 1. We also obtain a generating function for the sum of the degrees of the unipotent characters of $\mathrm{Sp}(2n, \mathbb{F}_q)$ , or of $\mathrm{SO}(2n+1, \mathbb{F}_q)$ , for any prime power $q$ .

Keywords

finite symplectic groups real representations irreducible representations Frobenius-Schur indicators unipotent characters characteristic two

Cite

@article{arxiv.1708.07176,
  title  = {Real representations of finite symplectic groups over fields of characteristic two},
  author = {C. Ryan Vinroot},
  journal= {arXiv preprint arXiv:1708.07176},
  year   = {2017}
}

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