Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry
| dc.creator | Yakimov, Milen | |
| dc.date | 2009-02-12 | |
| dc.date.accessioned | 2026-07-07T12:41:01Z | |
| dc.date.available | 2026-07-07T12:41:01Z | |
| dc.description | We prove that the standard Poisson structure on the Grassmannian Gr(k, n) is invariant under the action of the Coxeter element c =(1 2 ... n). In particular, its symplectic foliation is invariant under c. As a corollary, we obtain a second, Poisson geometric proof of the result of Knutson, Lam, and Speyer that the Coxeter element c interchanges the Lusztig strata of Gr(k, n). We also relate the main result to known anti-invariance properties of the standard Poisson structures on cominuscule flag varieties. | |
| dc.description | 5 pages, AMS Latex | |
| dc.identifier | https://arxiv.org/abs/0902.2181 | |
| dc.identifier | http://arxiv.org/abs/0902.2181 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219630 | |
| dc.subject | Combinatorics | |
| dc.subject | Symplectic Geometry | |
| dc.title | Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry | |
| dc.type | text |