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One-dimensional representations of W-algebras

Date: 
Friday 26th June 2009 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Premet conjectured that any (finite) W-algebra has a one-dimensional representation. The goal of this talk is to explain results of the speaker towards this conjecture. We will start giving a sketch of proof for the classical Lie algebras. Then we explain a reduction to rigid nilpotent elements using a parabolic induction functor. Finally, we will explain how using the Brundan-Goodwin-Kleshchev category O one can try to describe one-dimensional representations of W-algebras associated to rigid elements in exceptional Lie algebras.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons