Published 2010 | Version Published + Accepted Version
Journal Article Open

Any flat bundle on a punctured disc has an oper structure

Abstract

We prove that any flat G-bundle, where G is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric Langlands correspondence proposed in {FG}. Our proof uses certain deformations of the affine Springer fibers which could be of independent interest. As a byproduct, we construct representations of affine Weyl groups on the homology of these deformations generalizing representations constructed by Lusztig.

Additional Information

© 2010 International Press of Boston, Inc. Received by the editors December 9, 2008. Revision received December 9, 2009. Supported by DARPA and AFOSR through the grant FA9550-07-1-0543. We thank D. Arinkin for suggesting a simpler proof of Proposition 6. E.F. thanks Fondation Sciences Mathématiques de Paris for its support and the group "Algebraic Analysis" at Université Paris VI for hospitality. X.Z. thanks Zhiwei Yun for useful discussions.

Attached Files

Published - MRL-2010-0017-0001-a003.pdf

Accepted Version - 0811.3186v2.pdf

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Additional details

Identifiers

Eprint ID
49873
Resolver ID
CaltechAUTHORS:20140919-152325394

Related works

Funding

Defense Advanced Research Projects Agency (DARPA)
Air Force Office of Scientific Research (AFOSR)
FA9550-07-1-0543
Fondation Sciences Mathématiques de Paris

Dates

Created
2014-09-24
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Updated
2021-11-10
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Physics Department