Lectures on Wakimoto modules, opers and the center at the critical level
Abstract
Wakimoto modules are representations of affine KacMoody algebras in Fock modules over infinitedimensional Heisenberg algebras. In these lectures we present the construction of the Wakimoto modules from the point of view of the vertex algebra theory. We then use Wakimoto modules to identify the center of the completed universal enveloping algebra of an affine KacMoody algebra at the critical level with the algebra of functions on the space of opers for the Langlands dual group on the punctured disc. These results were originally obtained by B. Feigin and the author.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2002
 arXiv:
 arXiv:math/0210029
 Bibcode:
 2002math.....10029F
 Keywords:

 Quantum Algebra;
 Algebraic Geometry
 EPrint:
 85 pages, Latex