A geometric proof of the Feigin-Frenkel theorem

Raskin, Sam

doi:10.1090/S1088-4165-2012-00417-4

A geometric proof of the Feigin-Frenkel theorem
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by Sam Raskin

Represent. Theory 16 (2012), 489-512

DOI: https://doi.org/10.1090/S1088-4165-2012-00417-4

Published electronically: September 20, 2012

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Previous version: Original version posted September 20, 2012

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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