Generalized zeta integrals on real prehomogeneous vector spaces
Time: Mon, 9 Sep 2019, 13:30-15:05
Place: Ningzhai (宁斋) W11
Speaker: Wenwei Li (Peking University)
Abstract:
The Godement-Jacquet zeta integrals and Sato’s prehomogeneous zeta integrals share a common feature: they both involve Schwartz functions and Fourier transforms on prehomogeneous vector spaces. In this talk I will sketch a common generalization in thelocal Archimedean case. Specifically, for a reductive prehomogeneous vector space which is also a spherical variety, I will define the zeta integrals of generalized matrix coefficients of admissible representations against Schwartz functions, prove their convergenceand meromorphic continuation, and establish the local functional equation. Our arguments are based on various estimates on generalized matrix coefficients and Knop’s work on invariant differential operators.