Lifting representations of finite reductive groups II: Explicit conorms

Details Lifting representations of finite reductive groups II: Explicit conorms Lifting representations of finite reductive groups II: Explicit conorms

2011-09-05

arxiv.org/abs/1109.0794v1

Mathematics

Representation Theory

Scientific paper

Let $k$ be a field, $\tilde{G}$ a connected reductive $k$-quasisplit group, $\Gamma$ a finite group that acts on $\tilde{G}$ via $k$-automorphisms satisfying a quasi-semisimplicity condition, and $G$ the connected part of the group of $\Gamma$-fixed points of $\tilde{G}$, also assumed $k$-quasisplit. In an earlier work, the authors constructed a canonical map $\hat{\mathcal{N}}$ from the set of stable semisimple conjugacy classes in the dual $G^*(k)$ to the set of such classes in $\tilde{G}^*(k)$. We describe several situations where $\hat{\mathcal{N}}$ can be refined to an explicit function on points, or where it factors through such a function.

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