论文标题
加倍构造：Sumphectic组覆盖物的完整L功能
Doubling Constructions: the complete L-function for coverings of the symplectic group
论文作者
论文摘要
我们开发了$ m $ - 折中央扩展的广义加倍方法的局部理论，$ sp_ {2n}^{（m）} $ symplectic group的Matsumoto。我们定义本地$γ$ - ，$ l $ - 和$ε$ - $ $ - $ sp_ {2n}^{（m）} \ times \ wideTilde {gl} _k $的真实表示形式，并证明其基本属性在Shahidi的意义上。这里$ \ wideTilde {gl} _k $是$ gl_k $的中心扩展名，在langlands-shahidi方法中，用于覆盖$ sp_ {2n} \ times gl_k $的组。然后，我们为Cuspidal表示构建完整的$ L $ function，并证明其全局功能方程。可能的应用程序包括分类结果和shimura类型的表示从覆盖组到一般线性组的升降（在此处以$ M = 2 $的范围勾勒出全球升降机）。
We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $γ$-, $L$- and $ε$-factors for pairs of genuine representations of $Sp_{2n}^{(m)}\times\widetilde{GL}_k$ and prove their fundamental properties, in the sense of Shahidi. Here $\widetilde{GL}_k$ is the central extension of $GL_k$ arising in the context of the Langlands--Shahidi method for covering groups of $Sp_{2n}\times GL_k$. We then construct the complete $L$-function for cuspidal representations and prove its global functional equation. Possible applications include classification results and a Shimura type lift of representations from covering groups to general linear groups (a global lift is sketched here for $m=2$).
