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Any flat bundle on a punctured disc has an oper structure

Frenkel, Edward and Zhu, Xinwen (2010) Any flat bundle on a punctured disc has an oper structure. Mathematical Research Letters, 17 (1). pp. 27-37. ISSN 1073-2780.

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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.

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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.
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Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-07-1-0543
Fondation Sciences Mathématiques de ParisUNSPECIFIED
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ID Code:49873
Deposited By: George Porter
Deposited On:24 Sep 2014 21:03
Last Modified:03 Oct 2019 07:18

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