Indecomposable fusion products Original Research Article

We analyse the fusion products of certain representations of the Virasoro algebra for c = −2 and c = −7 which are not completely reducible. We introduce a new algorithm which allows us to study the fusion product level by level, and we use this algorithm to analyse the indecomposable components of these fusion products. They form novel representations of the Virasoro algebra which we describe in detail.