Polynomial representation growth and the congruence subgroup problem
- Cite this article as:
- Lubotzky, A. & Martin, B. Isr. J. Math. (2004) 144: 293. doi:10.1007/BF02916715
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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.