Arithmetic Homogeneous Spaces

Given a higher rank arithmetic group (E.g. SL(3,Z)) it has r(n) complex irreducible representations of degree n. We will study the the rate of growth of r(n), the associated zeta function SUM(r(n)n^(-s)), its Euler factorisation etc. Some connections with subgroup growth, congruence subgroup property and super-rigidity will be shown. (Based on joint works with B. Martin and with M. Larsen.