A new family of modules over the Virasoro algebra

In this paper, we constructed a new family of Virasoro modules Ω(λ,α,h)Ω(λ,α,h) parameterized by complex numbers λ≠0λ≠0, α∈Cα∈C and a polynomial h(t)h(t). They are a special type of modules on which the non-central Cartan part acts freely of infinite rank. These modules are natural generalizations of the modules Ω(λ,α)Ω(λ,α) defined and studied in [5], [11] and [19]. We determine the sufficient and necessary conditions for them to be irreducible. When they are reducible, we also determine all their maximal submodules and corresponding simple quotients explicitly. For some special cases, we can determine all submodules.