The Gelfand-Zeitlin integrable system and its action on generic elements of gl(n) and so(n)
| dc.creator | Colarusso, Mark | |
| dc.date | 2008-11-06 | |
| dc.date.accessioned | 2026-07-07T10:16:20Z | |
| dc.date.available | 2026-07-07T10:16:20Z | |
| dc.description | In recent work Bertram Kostant and Nolan Wallach ([KW1], [KW2]) have defined an interesting action of a simply connected Lie group $A$ isomorphic to \mathbb{C}^{n\choose 2} on gl(n) using a completely integrable system derived from Gelfand-Zeitlin theory. In this paper we show that an analogous action of \mathbb{C}^{d} exists on the complex orthogonal Lie algebra so(n), where d is half the dimension of a regular adjoint orbit in so(n). In [KW1], Kostant and Wallach describe the orbits of $A$ on a certain Zariski open subset of regular semisimple elements in gl(n). We extend these results to the case of so(n). We also make brief mention of the author's results in [Col1], which describe all $A$-orbits of dimension {n\choose 2} in gl(n). | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0811.0835 | |
| dc.identifier | http://arxiv.org/abs/0811.0835 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173472 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 14L30; 14R20; 37K10; 53D17 | |
| dc.title | The Gelfand-Zeitlin integrable system and its action on generic elements of gl(n) and so(n) | |
| dc.type | text |