Polynomial representation growth and the congruence subgroup problem

Alexander Lubotzky*, Benjamin Martin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

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 languageEnglish
Pages (from-to)293-316
Number of pages24
JournalIsrael Journal of Mathematics
Volume144
DOIs
StatePublished - 2004

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