Special Orthogonal, Special Unitary, and Symplectic Groups as Products of Grassmannians
Abstract
Abstract. 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 [Formula: see text] is a product of two real Grassmannians, [Formula: see text] is a product of four complex Grassmannians, and [Formula: see text] or [Formula: see text] is a product of four symplectic Grassmannians over [Formula: see text] or [Formula: see text], respectively. Our proofs essentially require only standard matrix theory.
Fields of Study & Subjects
Finite Group Theory Research
Graph theory and applications
Mathematics and Applications
Publication details
- Journal / source
- SIAM Journal on Matrix Analysis and Applications
- Volume
- 47
- Issue
- 2
- Pages
- 954–975
- Publication date
- 23 June 2026
- Language
- EN