Published 2010
| Version Published + Accepted Version
Journal Article
Open
Any flat bundle on a punctured disc has an oper structure
Creators
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
Files
0811.3186v2.pdf
Additional details
Identifiers
- Eprint ID
- 49873
- Resolver ID
- CaltechAUTHORS:20140919-152325394
Related works
- Describes
- http://arxiv.org/abs/0811.3186 (URL)
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
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2014-09-24Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
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