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Discrete series representations, the Dirac operator and C*-algebra K-theory

Banff International Research Station for Mathematical Innovation and Discovery

This is an expository talk about C*-algebra K-theory for reductive groups. I’ll try to explain what it is, what it actually says about representation theory, and what else it suggests about representation theory, at least to a willing mind. The story begins with Harish-Chandra’s parametrization of the discrete series representations, and the realization of discrete series representations using the Dirac operator. I’ll discuss these things, and then touch on other parts of Harish-Chandra’s theory of tempered representations that are prominent from the K-theoretic point of view.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: Pennsylvania State University

2018-10-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67572

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/