Abstract
Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra [Formula: see text], where Vir is the Virasoro algebra and [Formula: see text] is a commutative associative unital algebra over [Formula: see text]. In this paper, we study the irreducibility problem for the tensor product of highest weight modules and intermediate modules for [Formula: see text]. Finally we found out a necessary and sufficient condition for such modules to be isomorphic.
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