The Geometry of Polygons in R^5 and Quaternions
| dc.creator | Foth, Philip | |
| dc.creator | Lozano, Guadalupe | |
| dc.date | 2002-02-17 | |
| dc.date | 2004-01-23 | |
| dc.date.accessioned | 2026-07-07T04:46:30Z | |
| dc.date.available | 2026-07-07T04:46:30Z | |
| dc.description | We consider the moduli space M_r of polygons with fixed side lengths in five-dimensional eucledian space. We analyze the local structure of its singularities and exhibit a real-analytic equivalence between M_r and a weighted quotient of the n-fold product of the quaternionic projective line HP^1 by the diagonal PSL(2,H)-action. We explore the relation between M_r and the fixed point set of an anti-symplectic involution on a GIT quotient Gr(2,4)^n/SL(4,C). We generalize the Gel'fand-MacPherson correspondence to more general complex Grassmannians and to the quaternionic context, and realize our space M_r as a quotient of a subspace in the quaternionic Grassmannian Gr_H(2,n) by the action of the group Sp(1)^n. We also give analogues of the Gel'fand-Tsetlin coordinates on the space of quaternionic Hermitean matrices and briefly describe generalized action-angle coordinates on M_r. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202162 | |
| dc.identifier | http://arxiv.org/abs/math/0202162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63356 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | The Geometry of Polygons in R^5 and Quaternions | |
| dc.type | text |