Decomposition of Marsden–Weinstein Reductions for Representations of Quivers

By W. Crawley‐Boevey. Compositio Mathematica, 2000

50 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/456b2e7f92237a30f3fd463220bed807ff5bb53a

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In Discrete Mathematics and Combinatorics

1. Mark D. Haiman
2. K. Nagao
3. W. Crawley‐Boevey
4. B. Keller
5. Daisuke Yamakawa
6. Ben Davison
7. T. Bridgeland
8. Vladimir Petrov Kostov

In Geometry and Topology

1. Mark D. Haiman
2. K. Nagao
3. W. Crawley‐Boevey
4. I. Losev
5. I. Gordon
6. V. Ginzburg
7. H. Nakajima
8. Vladimir Petrov Kostov

In Mathematical Physics

1. Mark D. Haiman
2. K. Nagao
3. W. Crawley‐Boevey
4. H. Nakajima
5. I. Losev
6. I. Gordon
7. Thomas Lam
8. James Haglund

Citations in the corpus

• Derived categories of small toric Calabi-Yau 3-folds and counting invariants (2008, background): “Aˆ N is vCv, where C is the Cartan matrix of type AˆN ([Nak94]). So vCv is nonnegative, which is the definition of the root vectors. The uniqueness follows from the irreducibility of the moduli space ([CB02]). The hyperplanes Wα := {ζ∈ ZQ0 | ζ· α= 0} (α∈ Λ) gives a new chamber structure on the space ”
• Normality of Marsden-Weinstein reductions for representations of quivers (2001, background): “Note that, as in [ 7 ], we consider NQ(λ, α) as a variety, that is, we endow it with the reduced scheme structure.”
• Combinatorics, symmetric functions, and Hilbert schemes (2002, result): “This fact, which is well-known to the experts, is a consequence of the McKay correspondence and results of Kronheimer and Nakajima [53], Nakajima [67], and Crawley-Boevey [14].”