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Free field realization of the twisted Heisenberg-Virasoro algebra and W(2,2)-algebra and applications to representation theory

We present a free field realisation of the Heisenberg-Virasoro VOA, and some of its highest weight modules. We see how irreducibility of tensor product of irreducible highest weight module and irreducible module from intermediate series affects the existence of non-trivial intertwining operators. By using the fusion rules of Heisenberg algebra we get soem intertwining operators for HVir. This is a join work with Dražen Adamović

Heisenberg-Virasoro algebra, intertwining operators

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