Irreducible twisted Heisenberg-Virasoro modules from tensor products

In this paper, we realize polynomial $H$-modules $Omega(lambda,alpha,beta)$ from irreducible twisted Heisenberg-Virasoro modules $A_{alpha,beta}$. It follows from $H$-modules $Omega(lambda,alpha,beta)$ and $mathrm{Ind}(M)$ that we obtain a class of natural non-weight tensor product modules $big(bigotimes_{i=1}^mOmega(lambda_i,alpha_i,beta_i)big)otimes mathrm{Ind}(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.