Geometry Seminar

 

Magic Square and Classification of Symmetric Spaces

Mr. Yongdong Huang

Department of Mathematics

The Chinese University of Hong Kong

Abstract

In this article we introduce and study the (i) Grassmannian, (ii) Lagrangian Grassmannian and (iii) double Lagrangian Grassmannian of subspaces in (A Ä B)n, where A and B are normed division algebras, that is R, C, H or O.

 

We show that every compact symmetric space X must be one of these Grassmannian spaces (up to a finite cover) or a compact Lie group. Furthermore, its noncompact dual symmetric space is the open submanifold of X consisting of spacelike linear subspaces.

 

This gives a simple and uniform description of all symmetric spaces. This is similar to Tits magic square description for simple Lie algebras.

 

Date:

December 7, 2006 (Thursday)

Time:

4:00 – 5:00pm

Place:

Room 517, Meng Wah Complex, HKU

 

 

 

All are welcome