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

Abstract

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 SU(n) of Agnihotri and the second author and Belkale on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.

Locations

• Annales de l’institut Fourier - View - PDF