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The decomposition of permutation module for infinite Chevalley groups. (English) Zbl 07344752

Summary: Let G be a connected reductive group defined over \(\mathbb{F}_q\), the finite field with \(q\) elements. Let B be a Borel subgroup defined over \(\mathbb{F}_q\). In this paper, we completely determine the composition factors of the induced module \(\mathbb{M}(\mathrm{tr})=\Bbbk \mathbf{G}\otimes_{\Bbbk\mathbf{B}}\mathrm{tr}\) (where tr is the trivial B-module) for any field \(\Bbbk\).

MSC:

20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
22E99 Lie groups
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References:

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