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A Note On A Symplectic Structure On The Space Of G-Monopoles, M Finkelberg, A Kuznetsov, N Markarian, I Mirkovic

Mathematics and Statistics Department Faculty Publication Series

Let G be a semisimple complex Lie group with a Borel subgroup B. Let X=G/B be the flag manifold of G. Let C=\PP¹ ' ¥Unknown control sequence '\PP' be the projective line. Let a Î H₂(\bX,\Bbb Z)Unknown control sequence '\bX'. The moduli space of G-monopoles of topological charge f is naturally identified with the space \CM_b(\bX,a)Unknown control sequence '\CM' of based maps from (C,X) to (X,B) of degree f. The moduli space of G-monopoles carries a natural hyperkähler structure, and hence a holomorphic symplectic structure. It was explicitly computed by R. Bielawski in …