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arXiv · 1107.3549

On Truncation of irreducible representations of Chevalley groups

Joachim Mahnkopf
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Abstract

We prove part of a higher rank analogue of the Mazur-Gouvea Conjecture. More precisely, let $\tilde{\bf G}$ be a connected, reductive ${\Bbb Q}$-split group and let $\Gamma$ be an arithmetic subgroup of $\tilde{\bf G}$. We show that the dimension of the slope $\alpha$ subspace of the cohomology of $\Gamma$ with values in an irreducible $\tilde{\bf G}$-module $L$ is bounded independently of $L$. The proof is elementary making only use of general principles of the representation theory of algebraic groups; it is based on consideration of certain truncations of irreducible representations of Chevalley groups.

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Joachim Mahnkopf. 2011-07-18. On Truncation of irreducible representations of Chevalley groups. https://arxiv.org/abs/1107.3549

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