On the symplectic structure of instanton moduli spaces |
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Authors: | Roger Bielawski Victor Pidstrygach |
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Affiliation: | aSchool of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom;bMathematisches Institut, Universitaet Goettingen, Goettingen 37073, Germany |
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Abstract: | We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R4. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces. |
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Keywords: | Instantons Quiver varieties Necklace algebra Symplectomorphisms |
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