Harmonic analysis and gamma functions on symplectic group

Abstract: We develop a new type of harmonic analysis on an extended symplectic group $G=\BG_m\times \Sp_2n$ over $p$-adic fields. It is associated with the Langlands $\gamma$-functions attached to irreducible admissible representations of $G(F)$ and the standard representation of the dual group. Our work can be viewed as an extension of the work of Godement-Jacquet (which is a generalization of Tate's thesis). We confirm a series of conjectures in the local theory of the Braverman-Kazhdan proposal in this setting. This is a joint work with D. Jiang and L. Zhang.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.