UC Santa Cruz

In this thesis, we compute the fusion rules among the irreducible modules of $V_L$ - the vertex operator algebra associated with a positive-definite even lattice $L$, and then use them to determine the irreducible decomposition of fusion products of irreducible $V_L$-modules. Specifically, we establish the following results: the fusion product of an untwisted $V_L$-module and another one of twisted type is a $V_L$-module of twisted type while the fusion product of two twisted $V_L$-modules is a sum of untwisted modules satisfying a certain relation.