Real representations of finite symplectic groups over fields of characteristic two

C. Ryan Vinroot

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arXiv · 1708.07176

Real representations of finite symplectic groups over fields of characteristic two

C. Ryan Vinroot

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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 $q$.

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BibTeX RIS

C. Ryan Vinroot. 2017-08-23. Real representations of finite symplectic groups over fields of characteristic two. https://arxiv.org/abs/1708.07176

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