Current Developments in Mathematics

Volume 2013

Rigidity in automorphic representations and local systems

Pages: 73 – 168

DOI: https://dx.doi.org/10.4310/CDM.2013.v2013.n1.a2

Author

Zhiwei Yun (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Abstract

We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect these local systems to be rigid. Examples of rigid automorphic representations from previous work are reviewed and more examples for $\mathrm{GL}_2$ are discussed in detail.

Keywords

rigid local systems, Langlands correspondence, automorphic representations

2010 Mathematics Subject Classification

Primary 11F70, 14D24. Secondary 14F05.

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Published 22 October 2014