Limit multiplicities, trace formulas and von Neumann dimensions

Abstract: Given a tower of lattices in a semisimple Lie group G, we will discuss the multiplicity of an irreducible representation of G in the L^2-space of functions on the quotients. We apply the Arthur-Selberg trace formulas to consider a bounded family of representations. We will show the limit multiplicities are exactly the von Neumann dimensions if the lattices are uniform or G is SL(n).

quantum computing and informationMathematicsPhysics

Audience: researchers in the topic

Mathematical Picture Language Seminar