Arithmetic groups have rational representation growth

Abstract

Let $\Gamma$ be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if $\Gamma$ has the congruence subgroup property, then the number of $n$-dimensional irreducible representations of $\Gamma$ grows like $n^\alpha$, where $\alpha$ is a rational number.

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Authors

Nir Avni

The Hebrew University of Jerusalem
Jerusalem 91904
Israel