New Characterization of Virasoro Modules Induced from Polynomial Subalgebras

Abstract

Abstract. In [OW2], Ondrus and Wiesner constructed a class of Virasoro modules that are induced from modules over the polynomial subalgebras of the Virasoro algebra. In the present paper, we give a new characterization of these modules using a special kind of modules constructed in [LQG] associated with Whittaker modules over the classical Witt algebra. As a consequence, we can reobtain the irreducibility of the modules in [OW2] as well as some other main results therein. This new point of view allows us to better understand these modules as well as the category of the Virasoro algebra, and to generalize these construction to some more general algebras.

Keywords: Virasoro algebra, Weyl algebra, Witt algebra, irreducible modules