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Geometric Langlands for Hypergeometric Sheaves


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


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Hypergeometric local systems, rigid automorphic data, Hecke eigensheaves, geometric Langlands.
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Prize for Excellence in Graduate Studies, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Zhu, Xinwen
Thesis Committee:
  • Graber, Thomas B. (chair)
  • Campbell, Christopher J.
  • Ramakrishnan, Dinakar
  • Zhu, Xinwen
Defense Date:24 May 2021
Non-Caltech Author Email:yilingfei12 (AT)
Record Number:CaltechTHESIS:05302021-184629266
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14205
Deposited By: Lingfei Yi
Deposited On:03 Jun 2021 23:54
Last Modified:08 Aug 2022 18:04

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