(1) Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
Abstract:
Let Γ be anS-arithmetic group in a semisimple group. We show that if Γ has the congruence subgroup property then the number of isomorphism
classes of irreducible complexn-dimensional characters of Γ is polynomially bounded. In characteristic zero, the converse is also true. We conjecture that
the converse also holds in positive characteristic, and we prove some partial results in this direction.
Dedicated to Andy Magid on the occasion of his sixtieth birthday