On the symplectic structure of instanton moduli spaces

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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.