On unitary representations of GL2n distinguished by the symplectic group
On unitary representations of GL2n distinguished by the symplectic group
复制标题
关于GL2n的辛群的酉表示
DOI：
10.1016/j.jnt.2006.10.018
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发表时间：
2007
影响因子：
0.7
通讯作者：
E. Sayag
中科院分区：
文献类型：
--
作者：
Omer Offen;E. Sayag
我们提供了 GLnover 的一系列表示，它是一个 p 进场，它允许辛群下的非零线性函数不变量（即 Sp(n) 可区分的表示）。这是 Heumos-Rallis 结果的概括。我们的证明使用全局方法。 [Omer Offen、Eitan Sayag、一般线性群的全局混合周期和局部 Klyachko 模型，已提交发表] 的结果意味着该族包含所有由辛群区分的不可约、酉表示。
We provide a family of representations of GLnover a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(n)-distinguished). This is a generalization of a result of Heumos–Rallis. Our proof uses global methods. The results of [Omer Offen, Eitan Sayag, Global mixed periods and local Klyachko models for the general linear group, submitted for publication] imply that the family at hand contains all irreducible, unitary representations that are distinguished by the symplectic group.