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12 May 2021    

Lewis Topley - Representations of finite W-algebras

A finite W-algebra is a non-commutative algebra which plays a key role in the representation theory of complex semisimple Lie algebras. It is constructed by quantum Hamiltonian reduction, and it gives a filtered quantisation of a transverse slice to a nilpotent orbit. Its representations have a lot to do with the geometry of the orbit closure and I will begin this talk by surveying some of the landmark results in this area. In the second part of the talk I will describe some of the techniques in my recent paper, in which I describe the variety of one dimensional representations associated to classical Lie algebras.