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

2006/03/23 by Maurizio Martino, Martino, Maurizio · 1 citation
Mathematics · #14B07 #16G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0603562

openalex publication_date 2006/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Geometry of the Moment Map for Representations of Quivers
• Decomposition of Marsden–Weinstein Reductions for Representations of Quivers

Cited by

• Nakajima quiver varieties in dimension four

Related

• Decomposition of Marsden-Weinstein reductions for representations of quivers
• Decomposition of Marsden–Weinstein Reductions for Representations of Quivers
• Geometry of the Moment Map for Representations of Quivers
• Representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities
• Symplectic reflection algebras