## Tuesday, January 8, 2013

In this paper we discuss structure of a tensor product $V_{\alpha,\beta}^{\prime} \otimes L(c,h)$ of irreducible module from intermediate series and irreducible highest weight module over Virasoro algebra. We generalize Zhang's irreducibility criterion from \cite{Zhang}, and show that irreducibility depends on existence of integral roots of a certain polynomial, induced by a singular vector in Verma module $V(c,h)$. A new type of irreducible $\operatorname*{Vir}$-module with infinite-dimensional weight subspaces is found. We show how existence of intertwining operator for modules over vertex operator algebra yields reducibility of $V_{\alpha,\beta}^{\prime} \otimes L(c,h)$ which is a completely new point of view to this problem. As an example, a complete structure of tensor product with minimal models $c=-22/5$ and $c=1/2$ is presented.