Arithmetic Groups Have Rational Representation Growth
classification
🧮 math.GR
math.RT
keywords
numberarithmeticrationalalgebraiccongruencefieldgroupgroups
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Let G be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if G has the congruence subgroup property, then the number of n-dimensional irreducible representations of G grows like n^a, where a is a rational number.
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