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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2008
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| Acceso en línea: | https://arxiv.org/abs/0805.1520 |
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| _version_ | 1866917854687789056 |
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| author | Orevkov, S. Yu. Orevkov, Yu. P. |
| author_facet | Orevkov, S. Yu. Orevkov, Yu. P. |
| 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0805_1520 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Agnihotri-Woodward-Belkale polytope and the intersection of Klyachko cones Orevkov, S. Yu. Orevkov, Yu. P. Combinatorics 15A42 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). |
| title | Agnihotri-Woodward-Belkale polytope and the intersection of Klyachko cones |
| topic | Combinatorics 15A42 |
| url | https://arxiv.org/abs/0805.1520 |