Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

Abstract

We introduce the infinite-dimensional Lie superalgebra $\mathcal{A}$ and construct a family of mappings from certain category of $\mathcal{A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.

21 pages, Latex

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