Gelfand-Zeitlin actions and rational maps
| dc.creator | Bielawski, Roger | |
| dc.creator | Pidstrygach, Victor | |
| dc.date | 2006-12-13 | |
| dc.date | 2006-12-16 | |
| dc.date.accessioned | 2026-07-07T07:35:28Z | |
| dc.date.available | 2026-07-07T07:35:28Z | |
| dc.description | We observe that the analogue of the Gelfand-Zeitlin action on gl(n,C), which exists on any symplectic manifold M with an Hamiltonian action of GL(n,C), has a natural interpretation as a residual action, after we identify M with a symplectic quotient of the product of M with T*GL(n-1,C)x...xT*GL(1,C). We also show that the Gelfand-Zeitlin actions on T*GL(n,C) and on the regular part of gl(n,C) can be identified with natural Hamiltonian actions on spaces of rational maps into full flag manifolds, while the Gelfand-Zeitlin action on the whole gl(n,C) corresponds to a natural action on a space of rational maps into the manifold of half-full flags in C^{2n}. | |
| dc.description | 24 pages; v.2 clarifies a confusing statement in the introduction | |
| dc.identifier | https://arxiv.org/abs/math/0612365 | |
| dc.identifier | http://arxiv.org/abs/math/0612365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120100 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53Dxx, 58D15, 14L30, 14R20 | |
| dc.title | Gelfand-Zeitlin actions and rational maps | |
| dc.type | text |