Gelfand-Zeitlin theory from the perspective of classical mechanics II
| dc.creator | Kostant, Bertram | |
| dc.creator | Wallach, Nolan | |
| dc.date | 2005-01-22 | |
| dc.date | 2005-03-30 | |
| dc.date.accessioned | 2026-07-07T05:16:18Z | |
| dc.date.available | 2026-07-07T05:16:18Z | |
| dc.description | In this paper, Part II, of a two part paper we apply the results of [KW], Part I, to establish, with an explicit dual coordinate system, a commutative analogue of the Gelfand-Kirillov theorem for M(n), the algebra of $n\times n$ complex matrices. The function field F(n) of M(n) has a natural Poisson structure and an exact analogue would be to show that F(n) is isomorphic to the function field of a $n(n-1)$-dimensional phase space over a Poisson central rational function field in $n$ variables. Instead we show that this the case for a Galois extension, $F(n, {\frak e})$, of F(n). The techniques use a maximal Poisson commutative algebra of functions arising from Gelfand-Zeitlin theory, the algebraic action of a $n(n-1)/2$--dimensional torus on $F(n, {\frak e})$, and the structure of a Zariski open subset of M(n) as a $n(n-1)/2$--dimensional torus bundle over a $n(n+1)/2$--dimensional base space of Hessenberg matrices. | |
| dc.description | 38 pages, plain tex | |
| dc.identifier | https://arxiv.org/abs/math/0501387 | |
| dc.identifier | http://arxiv.org/abs/math/0501387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73936 | |
| 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 II | |
| dc.type | text |