Anthony Henderson (University of Sydney)

Friday 17th March, 12.05-12.55pm, Carslaw 159

Quiver varieties and zero weight spaces

One of the most striking recent results in geometric representation theory is Nakajima's construction of the irreducible finite-dimensional representations of a simply-laced simple Lie algebra. As I will explain, each weight space is realized as the top homology of a remarkable `quiver variety'. A minor puzzle is that the zero weight space, which carries a representation of the Weyl group, is sometimes isomorphic to the representation on the top homology of a Springer fibre, which leads one to suspect an isomorphism between the varieties. This has been proved in type A by Maffei; I will discuss his isomorphism and the possible generalization to type D (joint work with K. MacGerty).