Abstract
Let Γ be an S-arithmetic group in a semisimple group. We show that if Γ has the congruence subgroup property then the number of isomorphism classes of irreducible complex n-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.
Original language | English |
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Pages (from-to) | 293-316 |
Number of pages | 24 |
Journal | Israel Journal of Mathematics |
Volume | 144 |
DOIs | |
State | Published - 2004 |