ABSTRACT Malikov 97-01589 The three topics of the proposal are: Harish-Chandra bimodules over affine Lie algebras, localization of admissible representations to the moduli of vector bundles and a Lie algebra of the group of homeomorphisms of the circle. The main tools to be employed are the Bernstein-Beilinson technique of localization of g-modules and related ideas originating in modern physics, for example Kazhdan-Lusztig tensoring and vertex operator algebras The last decade has seen a spectacular interplay of ideas coming from quantum physics and mathematics. This proposal is about the fusion of these ideas. The results might find application in conformal field theory, representation theory, geometry and low dimensional topology.
