GENERIC REPRESENTATIONS OF CLASSICAL LIE-SUPERALGEBRAS AND THEIR LOCALIZATION

We complete the study of arbitrary generic irreducible modules over a classical complex Lie superalgebra G initiated in [14] (where G was assumed to be of type I) by presenting a full description of the underlying G(0)-module of any such G-module. This enables us in particular to extend Beilinson-Bernstein's localization theorem to a certain full subcategory of the category of Q-modules with fixed central character and also to describe the image of the enveloping algebra U(G) in the global sections of a generic twisted ring of differential operators on any flag superspace. As an application we construct an infinite family of full subcategories of the category of G-modules with fixed generic atypical central character, each of which is equivalent to the category of G(0)-modules with fixed regular central character.