Harmonic Analysis and Gamma Functions on Symplectic Groups

Dihua Jiang, Zhilin Luo, Lei Zhang

Over a $p$-adic local field $F$ of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group $G={\mathbb{G}}_m\times {\mathrm{S}p}_{2n}$. It is a…