Geometric Langlands for Hypergeometric Sheaves

Citation

Yi, Lingfei (2021) Geometric Langlands for Hypergeometric Sheaves. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/257d-6p75. https://resolver.caltech.edu/CaltechTHESIS:05302021-184629266

Abstract

Generalized hypergeometric sheaves are rigid local systems on the punctured projective line with remarkable properties. In this paper, we construct the Hecke eigensheaves whose eigenvalues are the irreducible hypergeometric local systems in the setting of geometric Langlands program. We work in the framework of rigid automorphic data that is mainly due to Zhiwei Yun. The key point is to choose a proper collection of level structures and compute the space of automorphic forms that are equivariant with respect to these level structures. For those hypergeometric sheaves with wild ramification, we also generalize the construction of Hecke eigensheaves to other classical groups. We study part of their eigenvalues in the de Rham setting by giving an alternative construction of their Hecke eigen D-module using quantization of Hitchin system.

Thesis Files