Special orthogonal, special unitary, and symplectic groups as products of Grassmannians
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909912577081344 |
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| author | Lim, Lek-Heng Lu, Xiang Ye, Ke |
| author_facet | Lim, Lek-Heng Lu, Xiang Ye, Ke |
| contents | We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution matrices. We will show that $\operatorname{SO}(n)$ is a product of two real Grassmannians, $\operatorname{SU}(n)$ a product of four complex Grassmannians, and $\operatorname{Sp}(2n, \mathbb{R})$ or $\operatorname{Sp}(2n, \mathbb{C})$ a product of four symplectic Grassmannians over $\mathbb{R}$ or $\mathbb{C}$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special orthogonal, special unitary, and symplectic groups as products of Grassmannians Lim, Lek-Heng Lu, Xiang Ye, Ke Representation Theory Differential Geometry 14M15, 22E10, 22E15, 51A50 We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution matrices. We will show that $\operatorname{SO}(n)$ is a product of two real Grassmannians, $\operatorname{SU}(n)$ a product of four complex Grassmannians, and $\operatorname{Sp}(2n, \mathbb{R})$ or $\operatorname{Sp}(2n, \mathbb{C})$ a product of four symplectic Grassmannians over $\mathbb{R}$ or $\mathbb{C}$ respectively. |
| title | Special orthogonal, special unitary, and symplectic groups as products of Grassmannians |
| topic | Representation Theory Differential Geometry 14M15, 22E10, 22E15, 51A50 |
| url | https://arxiv.org/abs/2501.18172 |