English

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}
}