by  S.Yu. Orevkov   and   Yu.P. Orevkov

Abstract:

Agnihotri-Woodward-Belkale polytope $\Delta$ (resp. Klyachko cone K ) is the set of solutions of the multiplicative (resp. additive) Horn's problem, i.e., the set of triples of spectra of special unitary (resp. traceless Hermitian) n x n matrices satisfying AB = C (resp. A + B = C). K is the tangent cone of $\Delta$ at the origin. The group G = (Z/nZ) + (Z/nZ) acts naturally on $\Delta$.

In this note, we report on a computer calculation which shows that $\Delta$ coincides with the intersection of g K, g in G, for n < 15 but does not coincide for n =15 .

Our motivation was an attempt to understand how to solve the multiplicative Horn problem in practice for given conjugacy classes in SU(n).