Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities

Details Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities

2006-03-23

arxiv.org/abs/math/0603562v1

Mathematics

Representation Theory

28 pages, no figures

Scientific paper

We investigate the Poisson geometry of the Marsden-Weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver. We show that the stratification by representation type equals the stratification by symplectic leaves. The deformed symplectic quotient singularities - spectra of centres of symplectic reflection algebras associated to a wreath product - are shown to be isomorphic to reductions of a certain quiver. This establishes a method to calculate when these deformations are smooth. Furthermore, the isomorphism identifies symplectic leaves and so one can give a description of their symplectic leaves in terms of roots of the quiver.

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