New irreducible tensor product modules for the Virasoro algebra

In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\mathrm{\Omega }(\lambda ,\alpha ,h)$ defined in \cite{CG}, with irreducible highest weight modules $V(\theta ,h)$ or with irreducible Virasoro modules Ind${}_{\theta }(N)$ defined in \cite{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. These modules are not isomorphic to any other known irreducible Virasoro modules.