| Abstract: |
We will try to motivate the study of finite W-algebras as a natural part of Lie theory connected to many other classical objects, such as Whittaker modules, primitive ideals, canonical bases, polynomial representations of GL(n). We will explain how the category of finite dimensional modules over a W-algebra of type A categorifies polynomial representations of GL(n) and sketch a higher level Schur-Weyl duality between finite W-algebras and (degenerate) cyclotomic Hecke algebras. W-algebras are generalizations of the Virasoro algebra and are useful in conformal field theory.
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