New Irreducible Virasoro Modules From Tensor Products

Virasoro algebra is one of the most important infinite dimensional Lie algebra, and the Virasoro algebra theory has been widely used in theoretical physics, mathematical physics and other mathematical branches, for example, string theory, conformal field theory, vertex algebras, and so on. In this paper, we study the tensor products of two classes of Virasoro modules.For any complex numbers λ,6, λ≠0, one can define the Virasoro module Ω(λ,b), see [8,15]. In [22], Haijun Tan and Kaiming Zhao study the tensor products of Ω(λ,b) with the irreducible Virasoro module on which all dk act locally finitely for sufficiently large k ε Z. In [3], Hongjia Chen and Xiangqian Guo defined a new class of Virasoro modules Ω(λ, α.h.), where λ, a are complex numbers, λ≠ 0 and h(t) is a polynomial in t and this Virasoro module Ω(λ, a, h) is similar to Ω(λ, b). In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules Ω(λ, α, h) with the irreducible Virasoro modules on which all dk act locally finitely for sufficiently large k € Z. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible and determine the necessary and sufficient conditions for two of them to be isomorphic. Then we prove that these modules are not isomorphic to other known non-weight Virasoro modules, and we obtain a new class of irreducible Virasoro modules.