Geodesic
The Agnihotri--Woodward--Belkale Polytope and Klyachko Cones
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 101-107.

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The Agnihotri–Woodward–Belkale polytope $\Delta$ (resp., the Klyachko cone $\mathscr K$) is the set of solutions of the multiplicative (resp., additive) Horn problem, i.e., the set of triples of spectra of special unitary (resp. traceless Hermitian) $n\times n$ matrices satisfying $AB=C$ (resp. $A+B=C$). The set $\mathscr K$ is the tangent cone of $\Delta$ at the origin. The group $G=\mathbb Z_n\oplus\mathbb Z_n$ acts naturally on $\Delta$. In this note, we report on a computer calculation showing that $\Delta$ coincides with the intersection of $g\mathscr K$, $g\in G$, for $n\le 14$ but does not coincide with it for $n=15$. Our motivation was an attempt to understand how to solve the multiplicative Horn problem in practice for given conjugacy classes in $SU(n)$.
Keywords: unitary matrix, Weyl chamber, Horn problem, Gromov–Witten invariants, Littlewood–Richardson coefficients
Mots-clés : conjugacy class, Schubert calculus, Klyachko cone. 
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S. Yu. Orevkov; Yu. P. Orevkov. The Agnihotri--Woodward--Belkale Polytope and Klyachko Cones. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 101-107. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a10/

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