Root games on Grassmannians
| dc.creator | Purbhoo, Kevin | |
| dc.date | 2003-10-08 | |
| dc.date | 2007-05-18 | |
| dc.date.accessioned | 2026-07-07T08:02:07Z | |
| dc.date.available | 2026-07-07T08:02:07Z | |
| dc.description | We recall the root game, introduced in an earlier paper, which gives a fairly powerful sufficient condition for non-vanishing of Schubert calculus on a generalised flag manifold G/B. We show that it gives a necessary and sufficient rule for non-vanishing of Schubert calculus on Grassmannians. In particular, a Littlewood-Richardson number is non-zero if and only if it is possible to win the corresponding root game. More generally, the rule can be used to determine whether or not a product of several Schubert classes on Gr_l(n) is non-zero in a manifestly symmetric way. Finally, we give a geometric interpretation of root games for Grassmannian Schubert problems. | |
| dc.description | 21 pages, 5 figures. Final version | |
| dc.identifier | https://arxiv.org/abs/math/0310103 | |
| dc.identifier | http://arxiv.org/abs/math/0310103 | |
| dc.identifier | Journal of Algebraic Combinatorics, 25 (2007) no. 3, 239-258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129127 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N15 | |
| dc.title | Root games on Grassmannians | |
| dc.type | text |