The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n,C)
| dc.creator | Harada, Megumi | |
| dc.date | 2004-04-27 | |
| dc.date.accessioned | 2026-07-07T05:07:45Z | |
| dc.date.available | 2026-07-07T05:07:45Z | |
| dc.description | Gel'fand and Cetlin constructed in the 1950s a canonical basis for a finite-dimensional representation V(λ) of U(n,\C) by successive decompositions of the representation by a chain of subgroups. Guillemin and Sternberg constructed in the 1980s the Gel'fand-Cetlin integrable system on the coadjoint orbits of U(n,\C), which is the symplectic geometric version, via geometric quantization, of the Gel'fand-Cetlin construction. (Much the same construction works for representations of SO(n,\R).) A. Molev in 1999 found a Gel'fand-Cetlin-type basis for representations of the symplectic group, using essentially new ideas. An important new role is played by the Yangian Y(2), an infinite-dimensional Hopf algebra, and a subalgebra of Y(2) called the twisted Yangian Y^{-}(2). In this paper we use deformation theory to give the analogous symplectic-geometric results for the case of U(n,\H), i.e. we construct a completely integrable system on the coadjoint orbits of U(n,\H). We call this the Gel'fand-Cetlin-Molev integrable system. | |
| dc.description | 33 pages; 3 figures; 2 appendices | |
| dc.identifier | https://arxiv.org/abs/math/0404485 | |
| dc.identifier | http://arxiv.org/abs/math/0404485 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70983 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 70H06 (Primary); 37J15, 17B10 (Secondary) | |
| dc.title | The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n,C) | |
| dc.type | text |