The Gieseker space is a generalization of the Hilbert point scheme

Raphaël Paegelow (University of Lille)

Wednesday 19th March 16:00-17:00 Maths 311B

Abstract

We will present combinatorial links between the irreducible components of the locus of fixed points of the Gieseker space and the block theory of the Ariki-Koike algebra. First, we will provide a description of the locus of fixed points in terms of Nakajima quiver varieties over the McKay quiver of type A. We will explain the hidden combinatorics of cores of charged multipartitions, as defined by Fayers and developed by Jacon and Lecouvey, on the Gieseker side. In addition, we will present a new way to compute the multicharge associated with the core of a charged multipartition.
Finally, if time permits, we will also explain how the notion of core blocks, discovered by Fayers, can be interpreted geometrically using the deep connection between quiver varieties and affine Lie algebras.

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