BIMSA-YMSC Tsinghua Number Theory Seminar | On basic functions for GL_n

Abstract

Let G be a reductive group over a local field F. The basic functions are certain spherical functions defined on G(F), whose Satake transform gives rise to the unramified L factors for an algebraic representation $\rho$ of the Langlands dual group ${^L}G$. They play important roles in the integral representation of global L functions. In general, the structure of such functions is not well understood. In this talk, I will explain how to represent such functions as an integration of certain characteristic functions over the L-monoid for GL_n.

Speaker

Dr. DENG Taiwang has joined BIMSA in November 2022 as an Assistant Professor. His research interests are in the Langlands program (broadly speaking, the arithmetic, analytic and representation aspects of it). He obtained a Phd in Mathematics from the University of Paris 13. Previously, he has held the postdoctorial positions in Bonn University, the Max Planck Institute of Mathematics in Bonn and Tsinghua University.