Number Theory and Representation Theory Seminar: Wavefront Sets and Generic L-parcket

Venue: Lecture Hall, Institute For Advanced Study in Mathematics, Zijingang Campus

Speaker: Prof. Zhang Lei, National University of Singapore

Abstract: In this talk, we introduce a notion of arithmetic wavefront sets for admissible representations of classical groups over local fields of characteristic 0. Conjecturally, via local Langlands correspondence, this arithmetic wavefronts coincide with the classical wavefront sets in sense of Harish-Chandra characters. Hence this conjecture proposes an algorithm to explicate the wavefront sets of representations in generic L- packets, by computing local symplectic root numbers. In particular, we verify the analogue conjectures over finite fields. This is a joint project with Dihua Jiang (The University of Minnesota), Dongwen Liu (Zhejiang University), Zhicheng Wang (Soochow University).