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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2008
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/0805.1520 |
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Table of Contents:
- Agnihotri-Woodward-Belkale polytope $Δ$ (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) $n\times n$ matrices satisfying $AB=C$ (resp. $A+B=C$). $K$ is the tangent cone of $Δ$ at the origin. The group $G=\Bbb Z_n \oplus \Bbb Z_n$ acts naturally on $Δ$. In this note, we report on a computer calculation which shows that $Δ$ coincides with the intersection of $gK$, $g\in G$, for $n\le 14$ 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).