A positive proof of the Littlewood-Richardson rule using the octahedron recurrence.
Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants
The set of conjugacy classes appearing in a product of conjugacy classes in a compact, -connected Lie group 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 , where is the complexification of and is a maximal parabolic subgroup. This generalizes the results for of Agnihotri and the second author and Belkale on...
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