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Some applications of vertex Algebras to representation theory of infinite-dimensional Lie algebras

We discuss reducibility of tensor product of irreducible highest weight modules and irreducible module from intermediate series over the Virasoro algebra. Reducibility of these modules is related to the existence of intertwining operators among highest weight modules. In particular, the most interesting cases are those involving minimal models. Similar problem is discussed over some extensions of Virasoro algebra as well.

vertex algebras, infinite-dimensional Lie algebras, Virasoro algebra

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