Contragredients and a multiplicity one theorem for general spin groups
Contragredients and a multiplicity one theorem for general spin groups
复制标题
DOI：
10.1007/s00209-023-03228-3
复制
发表时间：
2021-04
影响因子：
0.8
通讯作者：
Melissa Emory;Shuichiro Takeda
中科院分区：
文献类型：
--
作者：
Melissa Emory;Shuichiro Takeda
每个正交群都有一个非平凡的扩张，我们称之为。的单位分量是更熟悉的，一般的自旋群。本文证明了特征为零的非阿基米德局部域上不可约容许表示的限制是多重自由的，并证明了类似的定理。我们的证明使用的方法Aizenbud，Gourevitch，Rallis和Schiffman，谁证明了类似的定理，和Waldspurger，谁证明了。我们还给出了一个明确的描述的contragradient的不可约的容许表示的和，这是需要将他们的方法应用到我们的情况。
Each orthogonal grouphas a nontrivial-extension, which we call. The identity component ofis the more familiar, the general Spin group. We prove that the restriction toof an irreducible admissible representation ofover a nonarchimedean local field of characteristic zero is multiplicity free and also prove the analogous theorem for. Our proof uses the method of Aizenbud, Gourevitch, Rallis and Schiffman, who proved the analogous theorem for, and of Waldspurger, who proved that for. We also give an explicit description of the contragredient of an irreducible admissible representation ofand, which is needed to apply their method to our situations.