A Geometric Proof of the Feigin-Frenkel Theorem

Details A Geometric Proof of the Feigin-Frenkel Theorem A Geometric Proof of the Feigin-Frenkel Theorem

2011-06-15

arxiv.org/abs/1106.3112v1

Mathematics

Representation Theory

Scientific paper

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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