Irreducible Virasoro modules from irreducible Weyl modules

We use Block's results to classify irreducible modules over the differential operator algebra C[t,t−1,ddt]. From modules A   over C[t,t−1,ddt] and using the “twisting technique” we construct a class of modules AbAb over the Virasoro algebra for any b∈Cb∈C. These new Virasoro modules are generally not weight modules. The necessary and sufficient conditions for AbAb to be irreducible are obtained. Then we determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. Many interesting examples for such irreducible Virasoro modules with different features are provided at the end of the paper. In particular the class of irreducible Virasoro modules Ω(λ,b)Ω(λ,b) for any λ∈C⁎λ∈C⁎ and any b∈Cb∈C are defined on the polynomial algebra C[x]C[x].