A classification of irreducible Wakimoto modules for the affine Lie algebra $A_1^{(1)}$

Abstract

By using methods developed in arXiv:math/0602181 we study the irreducibility of certain Wakimoto modules for $\widehat{s{l}_2}$ at the critical level. We classify all $\chi \in \mathbb{C}((z))$ such that the corresponding Wakimoto module $W_{\chi }$ is irreducible. It turns out that zeros of Schur polynomials play important rule in the classification result.

14 pages, to appear in Contemporary Mathematics

References in corpus (3)

• Lectures on Wakimoto modules, opers and the center at the critical level
• Local Geometric Langlands Correspondence: the Spherical Case
• Algebras of twisted chiral differential operators and affine localization of $\mathfrak{g}$-modules

Cited by in corpus (2)

• Whittaker modules for the affine Lie algebra $A_1^{(1)}$
• The Verlinde formula in logarithmic CFT