Moduli of Vector Bundles on Curves with Parabolic Structures.

V.B. Mehta; C.S. Seshadri

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The set of conjugacy classes appearing in a product of conjugacy classes in a compact, $1$ -connected Lie group $K$ can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety $G / P$ , where $G$ is the complexification of $K$ and $P$ is a maximal parabolic subgroup. This generalizes the results for $S U (n)$ of Agnihotri and the second author...

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Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights...