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arXiv · 0812.4918

On the symplectic structure of instanton moduli spaces

Roger Bielawski·Victor Pidstrygach
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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 R^4. 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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Roger Bielawski, Victor Pidstrygach. 2009-03-20. On the symplectic structure of instanton moduli spaces. https://arxiv.org/abs/0812.4918

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