Polygon spaces and Quaternions
14:00 - 14:50
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
The study on geometry of spaces consisting of polygons with fixed side lengths has driven a remarkable interests in various research areas including symplectic geometry and algebraic geometry. In this talk, we revisit classical relations between polygon spaces in 3 dimensional Euclidean space and Grassmannian spaces over real and complex numbers and extend these to quaternions so as to relate polygons in 5 dimensional Euclidean space and Grassmannian spaces over quaternions via spin representation. We also discuss a hierarchical relation among Gassmanians and polygon spaces over real, complex and quaternions via involutions induced from complexification.