A finite field analogue of Jacquet's conjecture on local converse theorem
Abstract:
I will talk about the proof of the finite-field-analogue of Jacquet‘s conjecture on local converse theorem for cuspidal representations of general linear groups. More precisely, the set of twisted gamma factors of $\pi$, $$ \{\gamma(\pi\times \tau, \psi)\ |\ \tau \in \CG_t,\ 1\le t \le [\frac{n}{2}]\}, $$ together with a central character $\omega_\pi$, determine uniquely (up to isomorphism) the irreducible cuspidal representation $\pi$ of $\GL_n(\BF_q),$ where $\CG_t$ denotes the set of irreducible generic representations of $\GL_t(\BF_q).$
Tea Time: 3:30PM, R707