Current Developments in Mathematics

Volume 2013

Rigidity in automorphic representations and local systems

Pages: 73 – 168



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


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.


rigid local systems, Langlands correspondence, automorphic representations

2010 Mathematics Subject Classification

Primary 11F70, 14D24. Secondary 14F05.

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