The Gieseker space is a generalization of the Hilbert scheme of points.
We will present combinatorial correspondences between the irreducible components of the
fixed points locus of the Gieseker space and the block theory of the Ariki-Koike algebra. First,
we will describe the locus of fixed points in terms of Nakajima quiver varieties over the McKay
quiver of type A. Then, we will present how to recover the 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 a deep connection between quiver varieties and
affine Lie algebras.