Title : Representation zeta functions of arithmetic groups
Speaker: Uri Onn
Affiliation: Australian National University
Time: 14:00 Tuesday, 11 June, 2019
Location: 303-257
Abstract
Let G be a group and let r(n,G) denote the number of isomorphism classes of n-dimensional complex irreducible representations of G. Representation growth is a branch of asymptotic group theory that studies the asymptotic and arithmetic properties of the sequence (r(n,G)). Whenever this sequence grows polynomially one can associate to it a Dirichlet generating function, known as the representation zeta function of G. Larsen and Lubotzky proved that for arithmetic groups which have polynomial representation growth the associated zeta functions have an Euler product decomposition, thereby allowing local-global analysis. One can then apply a variety of tools such as the Kirillov orbit method, p-adic integration, Algebraic geometry, Model theory and Clifford theory. In this talk I will explain how these ingredients fit together to give some interesting properties of representation zeta functions associated to arithmetic and p-adic groups.

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