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arXiv · 1808.07116

Galois group action and Jordan decomposition of characters of finite reductive groups with connected center

Bhama Srinivasan·C. Ryan Vinroot
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Abstract

Let $\mathbf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism F. Given an irreducible complex character $\chi$ of $\mathbf{G}^F$ with its Jordan decomposition, and a Galois automorphism $\sigma \in \mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, we give the Jordan decomposition of the image ${^\sigma \chi}$ of $\chi$ under the action of $\sigma$ on its character values.

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Bhama Srinivasan, C. Ryan Vinroot. 2018-08-21. Galois group action and Jordan decomposition of characters of finite reductive groups with connected center. https://arxiv.org/abs/1808.07116

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