Vertex operator algebras and irreducibility of certain modules for affine Lie algebras

We find the connection between the representation theory of vertex operator algebra $L(k \Lambda_0)$ and the irreducibility of tensor products ${\oV} \otimes L(k \Lambda_0)$. In the case of affine Lie algebra $A_1 ^{(1)}$, on every admissible rational level we construct a family of irreducible modules having infinite-dimensional weight spaces.

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Published 1 January 1997