Yuly Billig
University of Carleton, Canada
Irreducible representations for the Lie algebra of vector fields on a torus.
Abstract: The goal of this work is to construct irreducible bounded weight modules for the Lie algebra of vector fields on a torus. These modules have a weight decomposition with finite-dimensional weight spaces and possess the property that the energy operator has spectrum bounded from below. We use generalized Wakimoto modules to give an explicit free-field realization of a family of such representations. The modules in this family are irreducible unless they belong to the chiral de Rham complex, introduced by Malikov, Schechtman and Vaintrob. This is a joint work with Vyacheslav Futorny.