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Representation Theory

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A geometric proof of the Feigin-Frenkel theorem

Author: Sam Raskin
Journal: Represent. Theory 16 (2012), 489-512
MSC (2010): Primary 17B65, 81R10, 14D24
Published electronically: September 20, 2012
Previous version: Original version posted September 20, 2012
MathSciNet review: 2972556
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Abstract: We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are certain de Rham local systems with extra structure) for the Langlands dual group. Our proof incorporates a construction of Beilinson and Drinfeld relating the Feigin-Frenkel isomorphism to (more classical) Langlands duality through the geometric Satake theorem.

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Additional Information

Sam Raskin
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138

Received by editor(s): June 12, 2011
Received by editor(s) in revised form: August 21, 2011, and January 3, 2012
Published electronically: September 20, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.