A Geometric Proof of the Feigin-Frenkel Theorem
Representation Theory
2011-06-17 v1 Algebraic Geometry
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1106.3112,
title = {A Geometric Proof of the Feigin-Frenkel Theorem},
author = {Sam Raskin},
journal= {arXiv preprint arXiv:1106.3112},
year = {2011}
}