题 目: The $n × (n-2) $ Local Converse Theorem for GL(n) Over p-adic Field
报告人： 粘珠凤 副教授 （台湾国立成功大学）
时 间: 2011年4月8日（星期五） 上午：10:00-11:00
地 点: 闵行校区数学系126室

摘 要：
The $n × m$ local converse theorem states: Let $\pi_1$, $\pi_2$be irreducible supercuspidal representations of GL(n, F), where F is a p-adic field. If the twisted local $\gamma$-factors are the same, i.e. $\gamma(s, \pi_1, \tau)=\gamma(s, \pi_2,\tau) $ for all irreducible supercuspidal representations $\tau$ of GL(k,F) with k = 1,2,…m, then $\pi_1$ and $\pi_2$ are equivalent.

This theorem characterizes the supercuspidal representations of GL(n,F) in terms of their \gamma-factors. A conjecture named after Jacquet predicts the verity of the $n × m$ local converse theorem for m=[n/2].

In this talk we will introduce Jeff Chen's work : The $n×(n-2)$ local converse theorem for $GL(n,F),$ which extends Henniart's result on $n×(n-1)$ local converse theorem (1993).