Speaker
Xiang Lu
(University of Chicago)
Description
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 $\text{SO}(n)$ is a product of two real Grassmannians, $\text{SU}(n)$ a product of four complex Grassmannians, and $\text{Sp}(2n, \mathbb{R})$ or $\text{Sp}(2n, \mathbb{C})$ a product of four symplectic Grassmannians over $\mathbb{R}$ or $\mathbb{C}$ respectively.
Authors
Lek-Heng Lim
(The University of Chicago)
Prof.
Ke Ye
(the Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Xiang Lu
(University of Chicago)