Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra
Date/Time:06 Nov 2019 10:00
Venue: S16 #03-09
Speaker: Tian Fangyang, National University of Singapore
Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra
This talk is a sequel of the report of Sakellaridis’ work on Spherical Varieties and Spherical Functions. Based on the geometric background which Zou Jialiang talked about last week, we will in this talk focus on the representation theoretic aspect of spherical varieties.
We will start from some Bruhat-Mackey theorem on spherical varieties (distributions on orbit-spaces) and its relation with the standard interwining operators. Under a suitable normalization of these intertwining operators via the Fourier transform (of Braverman-Kazhdan), we will present Sakellaridis Theorem 1.2.1 in his 2013 paper, which provides an explicit formula for the eigenfunction of the Hecke algebra in the space of spherical functions on a spherical variety.
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