Abstract:Generalised hypergeometric sheaves are rigid local systems on the punctured projective line with remarkable properties. Their study originated in the seminal work of Riemann on the Euler–Gauss hypergeometric function and has blossomed into an active field with connections to many areas of mathematics. In this paper, we construct the Hecke eigensheaves whose eigenvalues are the irreducible hypergeometric local systems, thus confirming a central conjecture of the geometric Langlands program for hypergeometrics. The key new concept is the notion of hypergeometric automorphic data. We prove that this automorphic data is generically rigid (in the sense of Zhiwei Yun) and identify the resulting Hecke eigenvalue with hypergeometric sheaves. The definition of hypergeometric automorphic data in the tame case involves the mirabolic subgroup, while in the wild case, semistable (but not necessarily stable) vectors coming from principal gradings intervene.

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中文翻译：

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超几何滑轮的几何朗兰兹

摘要：广义超几何滑轮是具有显着性质的穿孔射影线上的刚性局部系统。他们的研究起源于黎曼关于欧拉-高斯超几何函数的开创性工作，并发展成为一个活跃的领域，与数学的许多领域都有联系。在本文中，我们构造了特征值为不可约超几何局部系统的 Hecke 特征绳，从而证实了超几何的几何朗兰兹计划的中心猜想。关键的新概念是超几何自守数据的概念。我们证明这个自守数据是一般刚性的（在志伟的意义上），并用超几何滑轮识别得到的 Hecke 特征值。驯服情况下超几何自守数据的定义涉及到 mirabolic 子群，

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