Preservation of depth in the local geometric Langlands correspondence

Tsao Hsien Chen, Masoud Kamgarpour

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

It is expected that, under mild conditions, the local Langlands correspondence preserves depths of representations. In this article, we formulate a conjectural geometrisation of this expectation. We prove half of this conjecture by showing that the depth of a categorical representation of the loop group is greater than or equal to the depth of its underlying geometric Langlands parameter. A key ingredient of our proof is a new definition of the slope of a meromorphic connection, a definition which uses opers.

Original languageEnglish (US)
Pages (from-to)1345-1364
Number of pages20
JournalTransactions of the American Mathematical Society
Volume369
Issue number2
DOIs
StatePublished - 2017
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank C. Bremer, A. Molev, D. Sage, Z. Yun and X. Zhu for helpful conversations. The first author learned the definition of slope via opers, which is crucial in this paper, from X. Zhu. He is happy to thank him. The second author was supported by the Australian Research Council Discovery Early Career Research Award.

Publisher Copyright:
© 2016 American Mathematical Society.

Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

Keywords

  • Affine vertex algebras
  • Local geometric Langlands
  • Moy-Prasad theory
  • Opers
  • Segal-Sugwara operators
  • Slope of connections

Fingerprint Dive into the research topics of 'Preservation of depth in the local geometric Langlands correspondence'. Together they form a unique fingerprint.

Cite this