Israel Journal of Mathematics

, Volume 144, Issue 2, pp 293–316

Polynomial representation growth and the congruence subgroup problem


DOI: 10.1007/BF02916715

Cite this article as:
Lubotzky, A. & Martin, B. Isr. J. Math. (2004) 144: 293. doi:10.1007/BF02916715


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.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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