New irreducible tensor product modules for the Virasoro algebra (II)

In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\mathrm{\Omega }(\lambda ,\alpha ,h)$ and $\mathrm{\Omega }(\mu ,b)$ with irreducible highest weight modules $V(\theta ,h)$ or with irreducible Virasoro modules Ind${}_{\theta }(N)$ defined in [MZ2]. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. We also compare these modules with other known non-weight Virasoro modules.