Lectures on Wakimoto modules, opers and the center at the critical level

2002/10/02 by Edward Frenkel, Frenkel, Edward · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/0210029

85 pages, Latex

arxiv created 2002/11/06 · arxiv updated 2009/11/30

Abstract

Wakimoto modules are representations of affine Kac-Moody algebras in Fock modules over infinite-dimensional 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 Kac-Moody 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.

Cited by

• Irreduciblity of certain \widehat\mathfrak sl₂-modules of Wakimoto type
• The affine Brylinski filtration and \mathscrW-algebras
• Dualities of Gaudin models with irregular singularities for general linear Lie (super)algebras

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