A proof of the finite field analogue of Jacquet’s conjecture
A proof of the finite field analogue of Jacquet’s conjecture
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DOI：
10.1353/ajm.2014.0020
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发表时间：
2014-05
影响因子：
1.7
通讯作者：
Chufeng Nien
中科院分区：
文献类型：
--
作者：
Chufeng Nien
本文给出了一般线性群的倒丘表示的局部逆定理上Jacquet猜想的有限域模拟的证明。更准确地说，$\pi$、$$ \Big\{\gamma(\pi\times\tau,\psi)\mid \tau \in \scr{G}_t,\ 1\le t \le \Big[{n\over 2}\Big]\Big\}, $$的扭曲γ因子集和中心字符$\omega_\pi$，唯一地（直到同构）确定了${\rm GL}_n({\Bbb F}_q)$的不可约cuspidal表示$\pi$，其中${\cal G}_t$表示${\rm GL}_t({\Bbb F}_q)$的不可约一般表示集，${\Bbb F}_q$表示$q$元素的有限域。
In this paper, the proof of the finite-field-analogue of Jacquet's conjecture on local converse theorem for cuspidal representations of general linear groups is given. More precisely, the set of twisted gamma factors of $\pi$, $$ \Big\{\gamma(\pi\times\tau,\psi)\mid \tau \in \scr{G}_t,\ 1\le t \le \Big[{n\over 2}\Big]\Big\}, $$ together with a central character $\omega_\pi$, determine uniquely (up to isomorphism) the irreducible cuspidal representation $\pi$ of ${\rm GL}_n({\Bbb F}_q)$, where ${\cal G}_t$ denotes the set of irreducible generic representations of ${\rm GL}_t({\Bbb F}_q)$, and ${\Bbb F}_q$ denotes a finite field of $q$ elements.