The extraspecial case of the 𝑘(𝐺𝑉) problem

Gluck, David; Magaard, Kay

doi:10.1090/S0002-9947-01-02839-2

The extraspecial case of the $k(GV)\;$ problem
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by David Gluck and Kay Magaard PDF

Trans. Amer. Math. Soc. 354 (2002), 287-333 Request permission

Abstract:

Let $E$ be an extraspecial-type group and $V$ a faithful, absolutely irreducible $k[E]$-module, where $k$ is a finite field. Let $G$ be the normalizer in $GL(V)$ of $E$. We show that, with few exceptions, there exists a $v\in V$ such that the restriction of $V$ to $C_H(v)$ is self-dual whenever $H\le G$ and $(\vert H\vert , \vert V\vert )=1$.

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