Algebra and Topology Seminar

4pm Tuesday 1 November 2005
Anthony Henderson
University of Sydney

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).




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