论文标题
元素特殊特征的奇数特殊正交和符号群的局部匡威定理
The local converse theorem for odd special orthogonal and symplectic groups in positive characteristic
论文作者
论文摘要
令$ f $为非架构的本地字段，其特征与$ 2 $和$ g $不同，是一个奇怪的特殊正交组$ {\ rm so} _ {2r+1}（f）$，或者是符号组$ {\ rm sp sp} _ {2r} _ {2r}（f）$。在本文中，我们建立了$ g $的本地匡威定理。也就是说，如果给定两种不可约合的$ g $的不可约合的通用代表，则具有相同的中心特征，如果它们与$ {\ rm gl} _n（f）$的不可减至的超舒张代表扭曲的本地伽马因素，则所有$ 1 \ leq n \ leq n \ leq n \ leq n \ leq l leq r $具有相同的添加添加性符号，这些代表性是issomorphicals is is is is isomorphics。利用Cogdell，Shahidi和Tsai理论在部分Bessel函数上以及不可减至的通用表示的分类，我们以twists $ 1 \ leq n \ leq N \ leq 2r-1 $在Jiang and Soudry的工作中的障碍打破了障碍，并扩展了Q. Zhang的结果。
Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse theorem for $G$. Namely, for given two irreducible admissible generic representations of $G$ with the same central character, if they have the same local gamma factors twisted by irreducible supercuspidal representations of ${\rm GL}_n(F)$ for all $1 \leq n \leq r$ with the same additive character, these representations are isomorphic. Using the theory of Cogdell, Shahidi, and Tsai on partial Bessel functions and the classification of irreducible generic representations, we break the barrier on the rank of twists $1 \leq n \leq 2r-1$ in the work of Jiang and Soudry, and extend the result of Q. Zhang, which was achieved for all supercuspidal representations in characteristic $0$.
