%0 Journal Article
%T On Truncation of irreducible representations of Chevalley groups
%A Joachim Mahnkopf
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1107.3549v2