Xiang Tang: An index theorem on the tempered dual of a real reductive Lie group

Abstract

Let \(G\) be a (real reductive) Lie group. The tempered dual of \(G\) is the space of isomorphism classes of irreducible unitary \(G\)-representations that are contained in the (left) regular representation of \(G\) on \(L^2(G)\). In this talk, we will report our study on the geometry of the tempered dual. As an application, we will present an index theorem for proper cocompact \(G\)-actions. This talk is based on the joint works with Peter Hochs, Markus Pflaum, Hessel Posthuma, and Yanli Song.

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