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 $\widehat{sl_2}$ at the critical level. We classify all $\chi \in {\Bbb C}((z))$ 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.