Speaker: Trần Phan Quốc Bảo (University of Bern)
Time: 16:30 ngày 17/07/2025
Venue: Room 612, A6, Institute of Mathematics-VAST
Online (Join Zoom Meeting) tại link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1
Abstract: In this talk, I will present a unified framework for factoring symplectic and split-orthogonal matrices with holomorphic function coefficients using elementary matrices. Although the two factorizations share a nearly identical type of elementary matrices, a key distinction arises from the presence of the spinor norm in the orthogonal case. This additional invariant obstructs the straightforward diagonal factorization familiar from the symplectic setting. I will pinpoint this critical divergence, illustrate its impact on factorization of orthogonal matrices, and outline a strategy to deal with the diagonal orthogonal case, which relies on the famous paper "Clifford Algebras and Spinor Norms Over a Commutative Ring" of Hyman Bass and "Spin Groups Over a Commutative Ring and the Associated Root Data" of Hisatoshi Ikai. | 
