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Gelfand pairs and gamma factors mod ℓ

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

Robin Zhang

时间

2024年01月12日 16:00 至 17:00

地点

Tsinghua-Jingzhai-105

摘要

I will discuss two uniqueness phenomena in the representation theory of finite and compact groups. First, we have the classical complex theory of Gelfand pairs and its generalizations; this has many applications to number theory and automorphic forms, such as the uniqueness of Whittaker models and the non-vanishing of the central value of triple product L-functions. Second, we have the local converse theorems that say that irreducible representations have unique Rankin–Selberg gamma factors; in fact, the local Langlands correspondence for GL(n) can be uniquely characterized by gamma factors. We will show how both phenomena can be extended to positive characteristic using two techniques involving module projectivity. The second part of this talk is based on joint work with J. Bakeberg, M. Gerbelli-Gauthier, H. Goodson, A. Iyengar, and G. Moss.