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November 2018
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Events on Friday 10 August 2018

Equivariant Index, Traces and Representation Theory
11:10 Fri 10 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Hang Wang :: University of Adelaide

K-theory of C*-algebras associated to a semisimple Lie group can be understood both from the geometric point of view via Baum-Connes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. A K-theory generator can be viewed as the equivariant index of some Dirac operator, but also interpreted as a (family of) representation(s) parametrised by the noncompact abelian part in the Levi component of a cuspidal parabolic subgroup. Applying orbital traces to the K-theory group, we obtain the equivariant index as a fixed point formula which, for each K-theory generators for (limit of) discrete series, recovers Harish-Chandra’s character formula on the representation theory side. This is a noncompact analogue of Atiyah-Segal-Singer fixed point theorem in relation to the Weyl character formula. This is joint work with Peter Hochs.
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