Affinor structures in the oscillation theory

Boris N. Shapukov

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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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The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given.