Marvelous slices of orthogonal matrices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914303328649216 |
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| author | Brysiewicz, Taylor Gesmundo, Fulvio |
| author_facet | Brysiewicz, Taylor Gesmundo, Fulvio |
| contents | The space of $4 \times 4$ special orthogonal matrices with zeros on the diagonal decomposes into the union of $14$ irreducible surfaces whose intersections are beautifully encoded by the cuboctahedron. Using this decomposition, we exhibit a totally real witness set for $SO(4)$. We explain how to obtain a similar decomposition for $SO(5)$, where the $64$ components can be grouped to obtain such a correspondence with the face lattice of a $3$-polytope. We show that no such pattern exists for $SO(6)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02668 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Marvelous slices of orthogonal matrices Brysiewicz, Taylor Gesmundo, Fulvio Algebraic Geometry Combinatorics 15B10, 53A05, 52B10, 14Q65 The space of $4 \times 4$ special orthogonal matrices with zeros on the diagonal decomposes into the union of $14$ irreducible surfaces whose intersections are beautifully encoded by the cuboctahedron. Using this decomposition, we exhibit a totally real witness set for $SO(4)$. We explain how to obtain a similar decomposition for $SO(5)$, where the $64$ components can be grouped to obtain such a correspondence with the face lattice of a $3$-polytope. We show that no such pattern exists for $SO(6)$. |
| title | Marvelous slices of orthogonal matrices |
| topic | Algebraic Geometry Combinatorics 15B10, 53A05, 52B10, 14Q65 |
| url | https://arxiv.org/abs/2602.02668 |