W-algebras as Slodowy slice’s quantization

Stefania Mele (University of Glasgow)

Friday 5th June, 2015 16:00-17:00 Maths 416

Abstract

First of all, we’re going to define one of the main objects of this talk: the W-algebras U(g,e) (where g is a semisimple Lie algebra and e is a nilpotent element in g), following the Whittaker definition. Then, we will be interested in studying the structure of certain transverse slices to nilpotent orbits, called Slodowy slices. The main question we will answer to concerns the associated graded algebra of U(g, e) that turns out to correspond to the ring of functions of the Slodowy Slice. So, we will see a geometric link between these two objects we are focusing on and at the end, I’ll give just an example to see what happens if we intersect these slices with the closure of nilpotent orbits, giving a description of these last objects as quiver varieties. So, roughly speaking this talk will focus on these three main objects (W-algebra, Slodowy slice and an example of Nakajima quiver variety) and the main aim is that to analyse the links between them.

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