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Isaac Newton Institute for Mathematical Sciences

Finite W-algebras and their representations

Author: Ivan Losev (MIT)

Abstract

A (finite) W-algebra is a certain associative algebra constructed from a semisimple Lie algebra and its nilpotent element. The main reason why they are interesting is their relation to the representation theory of universal enveloping algebras.

In this course I am going to explain two different definitions of W-algebras: by Hamiltonian reduction (Premet, Gan-Ginzburg) and deformation quantization (I.L). Then I am going to explain category equivalence theorems relating representations of W-algebras and universal enveloping algebras and describe relation between primitive ideals.