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# Mathematical Research Letters

## Volume 4 (1997)

### Number 6

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

Pages: 809 – 821

DOI: http://dx.doi.org/10.4310/MRL.1997.v4.n6.a3

#### Author

#### Abstract

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.