Geometric Langlands for hypergeometric sheaves

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