There is a well-known correspondence (due to Mehta and Seshadri in the unitary case, and extended by Bhosle and Ramanathan to other groups), between the symplectic variety M-h of representations of the fundamental group of a punctured Riemann surface into a compact connected Lie group G, with fixed conjugacy classes h at the punctures, and a complex variety M-h of holomorphic bundles on the unpunctured surface with a parabolic structure at the puncture points. For G = SU(2), we build a symplectic variety P of pairs (representations of the fundamental group into G, "weighted frame" at the puncture points), and a corresponding complex variety P of moduli of "framed parabolic bundles", which encompass respectively all of the spaces M-h, M-h, in the sense that one can obtain M-h from P by symplectic reduction, and M-h from P by a complex quotient. This allows us to explain certain features of the toric geometry of the SU(2) moduli spaces discussed by Jeffrey and Weitsman, by giving the actual toric variety associated with their integrable system. [References: 21]
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