论文标题
$ \ mathrm {gl}（2）$的异国情调的单体结构和抽象的自动形式表示
Exotic Monoidal Structures and Abstractly Automorphic Representations for $\mathrm{GL}(2)$
论文作者
论文摘要
我们使用theta通信来研究$ \ mathrm {gl}（2）$的Godement-Jacquet和Jacquet-Langlands l功能之间的等价性。我们表明，结果比较实际上是$ \ mathrm {gl}（2）$模块的类别上的异国对称单体结构。 此外，这使我们能够构建一个抽象的自动形式表示的Abelian类别，其不可减至的对象是通常的自动形式表示。我们推测，此类别是研究$ \ mathrm {gl}（2）$的自然环境，并演示其基本属性。 本文是作者论文的一部分。
We use the theta correspondence to study the equivalence between Godement-Jacquet and Jacquet-Langlands L-functions for $\mathrm{GL}(2)$. We show that the resulting comparison is in fact an exotic symmetric monoidal structure on the category of $\mathrm{GL}(2)$-modules. Moreover, this enables us to construct an Abelian category of abstractly automorphic representations, whose irreducible objects are the usual automorphic representations. We speculate that this category is a natural setting for the study of automorphic phenomena for $\mathrm{GL}(2)$, and demonstrate its basic properties. This paper is a part of the author's thesis.
