Displaying similar documents to “Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.”

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Constantin Teleman, Christopher Woodward (2003)

Annales de l’institut Fourier

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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...

Indecomposable parabolic bundles

William Crawley-Boevey (2004)

Publications Mathématiques de l'IHÉS

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We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of × matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel’s theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the...