  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.
