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Fourier transform, orbital integral and character of representations

Banff International Research Station for Mathematical Innovation and Discovery

In 1980s, Connes and Moscovici studied index theory of G-invariant elliptic pseudo-differential operators acting on non-compact homogeneous spaces. They proved a $L^2$ -index formula using the heat kernel method, which is related to the discrete series representation of Lie groups. In this talk, I will discuss the orbital integral of heat kernel and its relation with Plancherel formula. This is a generalization of the analytic index studied by Connes-Moscovici to the limit of discrete series case. In a recent work by Hochs-Wang, they obained a fixed point theorem for the topogical side of the index. This is a joint work with Xiang Tang.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: Washington University at St.Louis

2019-04-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69441

Unreviewed

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