Featured Speaker :   Zhilin Luo (University of Minnesota)

Title :  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.

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