论文标题
通过几何兰兰兹的古典组的超几何滑轮
Hypergeometric sheaves for classical groups via geometric Langlands
论文作者
论文摘要
在上一篇论文中，第一和第三作者对超几何滑轮的几何兰兰兹信件进行了明确的实现，被认为是$ \ textrm {gl} _n $ - 局部系统。对于经典组$ \ check {g} $，某些超几何本地系统允许符号或正交结构，可以看作是$ \ check {g} $ - 本地系统。本文旨在实现这些$ \ check {g} $ - 本地系统的几何兰兰兹信件。我们从两个方面研究了这个问题。在第一种方法中，我们在Yun的框架中定义了经典群体$ g $的超几何自动形态数据，从Jakob-Yun的意义上讲，其本地组件是其本地组件之一。我们证明了自然假设下的超几何自动数据数据的刚性，这使我们能够定义$ \ check {g} $ - 本地系统$ \ mathcal {e} _ {\ check check {g}} $ on $ \ mathbb {g mathbb {g}在第二种方法（仅在DE RHAM设置中起作用）中，我们按照Beilinson-Drinfeld和Zhu进行了量化增强的受损Hitchin系统，并确定$ \ Mathcal {e} _ {\ check {g ch}} $，并用一定的$ \ check {g} $ - opers on $ \ mathbbbbbb {g}最后，我们将这些$ \ check {g} $ - Opers与超几何本地系统进行比较。
In a previous paper, the first and third authors gave an explicit realization of the geometric Langlands correspondence for hypergeometric sheaves, considered as $\textrm{GL}_n$-local systems. Certain hypergeometric local systems admit a symplectic or orthogonal structure, which can be viewed as $\check{G}$-local systems, for a classical group $\check{G}$. This article aims to realize the geometric Langlands correspondence for these $\check{G}$-local systems. We study this problem from two aspects. In the first approach, we define the hypergeometric automorphic data for a classical group $G$ in the framework of Yun, one of whose local components is a new class of euphotic representations in the sense of Jakob-Yun. We prove the rigidity of hypergeometric automorphic data under natural assumptions, which allows us to define $\check{G}$-local systems $\mathcal{E}_{\check{G}}$ on $\mathbb{G}_m$ as Hecke eigenvalues (in both $\ell$-adic and de Rham setting). In the second approach (which works only in the de Rham setting), we quantize an enhanced ramified Hitchin system, following Beilinson-Drinfeld and Zhu, and identify $\mathcal{E}_{\check{G}}$ with certain $\check{G}$-opers on $\mathbb{G}_m$. Finally, we compare these $\check{G}$-opers with hypergeometric local systems.
