Modular Gelfand pairs, multiplicity-free triples, and maybe some gamma factors

Abstract: The classical theory of Gelfand pairs and its generalizations over the complex numbers 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 a triple product $L$-function. With an eye towards similar applications in the modular setting, this talk presents an extension of the classical theory for representations of finite and compact groups to such representations over algebraically closed fields with arbitrary characteristic. Time permitting, I will also mention an analogue (joint with J. Bakeberg, M. Gerbelli-Gauthier, H. Goodson, A. Iyengar, and G. Moss) of the local converse theorem for Jacquet–Piatetski-Shapiro–Shalika gamma factors of mod $\ell \neq p$ representations of finite general linear groups.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

MIT number theory seminar

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