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Lie Superalgebras and Irreducibility of A_1 ^(1)-Modules at the Critical Level

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.

Lie superalgebras; vertex algebras; affine Lie algebras; critical level; Wakimoto modules

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