Virasoro representations and fusion for general augmented minimal models

In this paper, we present explicit results for the fusion of irreducible and higher rank representations in two logarithmically conformal models, the augmented c(2,3) = 0 model as well as the augmented Yang - Lee model at c(2,5)=- 22/5. We analyse their spectrum of representations which is consistent with the symmetry and associativity of the fusion algebra. We also describe the first few higher rank representations in detail. In particular, we present the first examples of consistent rank 3 indecomposable representations and describe their embedding structure. Knowing these two generic models we also conjecture the general representation content and fusion rules for general augmented c(p,q) models.