An analytic version of the Langlands correspondence for complex curves

Pavel Etingof, Edward Frenkel, David Kazhdan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

6 Scopus citations

Abstract

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct a function-theoretic version. In this paper we use the algebra of commuting global differential operators (quantum Hitchin Hamiltonians and their complex conjugates) on the moduli space of G-bundles of a complex algebraic curve to formulate a function-theoretic correspondence. We conjecture the existence of a canonical self-adjoint extension of the symmetric part of this algebra acting on an appropriate Hilbert space and link its spectrum with the set of opers for the Langlands dual group of G satisfying a certain reality condition, as predicted earlier by Teschner. We prove this conjecture for G = GL1 and in the simplest non-abelian case.

Original languageEnglish
Title of host publicationProceedings of Symposia in Pure Mathematics
PublisherAmerican Mathematical Society
Pages137-202
Number of pages66
DOIs
StatePublished - 2021

Publication series

NameProceedings of Symposia in Pure Mathematics
Volume103.2
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X

Bibliographical note

Publisher Copyright:
© 2021 by Pavel Etingof, Edward Frenkel, and David Kazhdan..

Fingerprint

Dive into the research topics of 'An analytic version of the Langlands correspondence for complex curves'. Together they form a unique fingerprint.

Cite this