Compact symmetric spaces, triangular factorization, and Poisson geometry
| dc.creator | Caine, Arlo | |
| dc.date | 2006-08-18 | |
| dc.date | 2006-11-21 | |
| dc.date.accessioned | 2026-07-07T07:21:54Z | |
| dc.date.available | 2026-07-07T07:21:54Z | |
| dc.description | Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each \u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson Lie group structure π_U on U. The Evens-Lu construction produces a (U,π_U)-homogeneous Poisson structure on X. By choosing the basepoint in X appropriately, X is presented as U/K where K is the fixed point set of an involution which stabilizes the triangular decomposition of \g. With this presentation, a connection is established between the symplectic foliation of the Evens-Lu Poisson structure and the Birkhoff decomposition of U/K. This is done through reinterpretation of results of Pickrell. Each symplectic leaf admits a natural torus action. It is shown that the action is Hamiltonian and the momentum map is computed using triangular factorization. Finally, local formulas for the Evens-Lu Poisson structure are displayed in several examples. | |
| dc.description | 27 pages, 3 figures, exposition substantially revised, proof of main results is given in the general case, submitted to the Journal of Lie Theory | |
| dc.identifier | https://arxiv.org/abs/math/0608454 | |
| dc.identifier | http://arxiv.org/abs/math/0608454 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115468 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53D17; 53C35; 17B20 | |
| dc.title | Compact symmetric spaces, triangular factorization, and Poisson geometry | |
| dc.type | text |