arXiv Open Access 2025

Special orthogonal, special unitary, and symplectic groups as products of Grassmannians

Lek-Heng Lim Xiang Lu Ke Ye

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.RT math.DG

Penulis (3)

Lek-Heng Lim

Xiang Lu

Ke Ye

Format Sitasi

APA MLA BibTeX

Lim, L., Lu, X., Ye, K. (2025). Special orthogonal, special unitary, and symplectic groups as products of Grassmannians. https://arxiv.org/abs/2501.18172

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓