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A Geometric Proof of the Feigin-Frenkel Theorem

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.

preprint2011arXivOpen access
Sam Raskin
math.RTmath.QAmath.AG
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Sam Raskin

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