Decomposition of Marsden–Weinstein Reductions for Representations of Quivers

2002/01/01 by William Crawley-Boevey · 10 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.1023/a:1013793632709

Abstract

We decompose the Marsden–Weinstein reductions for the moment map associated to representations of a quiver. The decomposition involves symmetric products of deformations of Kleinian singularities, as well as other terms. As a corollary we deduce that the Marsden–Weinstein reductions are irreducible varieties.

Citations

• Geometry of the Moment Map for Representations of Quivers

Cited by

• Chevalley restriction theorem for the cyclic quiver
• Nakajima quiver varieties in dimension four
• Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities
• The tame Deligne-Simpson problem
• Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras
• Derived categories of small toric Calabi-Yau 3-folds and counting invariants
• Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
• Quiver algebras, weighted projective lines, and the Deligne-Simpson problem
• Non-commutative covers and the modular group
• Rational Singularities for Moment Maps of Totally Negative Quivers. [europepmc]

Related

• Decomposition of Marsden-Weinstein reductions for representations of quivers
• Normality of Marsden-Weinstein reductions for representations of quivers
• Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities
• Geometry of the Moment Map for Representations of Quivers
• On the Reducedness of Quiver Schemes