Gelfand-Zeitlin theory from the perspective of classical mechanics. I
| dc.creator | Kostant, Bertram | |
| dc.creator | Wallach, Nolan | |
| dc.date | 2004-08-24 | |
| dc.date | 2004-09-08 | |
| dc.date.accessioned | 2026-07-07T05:11:33Z | |
| dc.date.available | 2026-07-07T05:11:33Z | |
| dc.description | A commutative Poisson subalgebra of the Poisson algebra of polynomials on the Lie algebra of n x n matrices over ${\Bbb C}$ is introduced which is the Poisson analogue of the Gelfand-Zeitlin subalgebra of the universal enveloping algebra. As a commutative algebra it is a polynomial ring in $n(n+1)/2$ generators, $n$ of which can be taken to be basic generators of the polynomial invariants. Any choice of the next $n(n-1)/2$ generators yields a Lie algebra of vector fields that generates a global holomorphic action of the additive group ${\Bbb C}^{n(n -1)/2}$. This paper proves several remarkable properties of this group action and relates it to the theory of orthogonal polynomials. | |
| dc.description | plain tex, 54 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408342 | |
| dc.identifier | http://arxiv.org/abs/math/0408342 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72279 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 14L30, 14R20, 33C45, 53D17 | |
| dc.title | Gelfand-Zeitlin theory from the perspective of classical mechanics. I | |
| dc.type | text |