Arithmetic groups have rational representation growth

Nir Avni*

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Let Γ be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if Γ has the congruence subgroup property, then the number of n-dimensional irreducible representations of Γ grows like nα, where α is a rational number.

Original languageEnglish (US)
Pages (from-to)1009-1056
Number of pages48
JournalAnnals of Mathematics
Volume174
Issue number2
DOIs
StatePublished - Sep 1 2011

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Arithmetic Groups
Congruence Subgroups
Semisimple Groups
Algebraic Groups
Irreducible Representation
Number field
n-dimensional
Congruence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Arithmetic groups have rational representation growth. / Avni, Nir.

In: Annals of Mathematics, Vol. 174, No. 2, 01.09.2011, p. 1009-1056.

Research output: Contribution to journalArticle

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