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D-modules on supermanifolds and localization theorems for Lie superalgebras

Mathematical Physics & Probability

Speaker: Vera Serganova, University of California, Berkeley
Location: 593 Kerr
Start time: Mon, Mar 5 2001, 3:10PM

Let G be a simple Lie algebra. Beilinson-Bernstein theorem states that there is an equivalence between the category of G-modules admotting given central character and the category of twisted D-modules in the flag variety G/B. We discuss this theorem in case when G is a simple classical Lie superalgebra. If a central character is generic then generalization of the theorem is straightforward. However the most interesting case is when a central character is degenrate (called atypical). We discuss this case in detail and see possible applications to representation theory.