The crystal structure on the set of Mirkovic-Vilonen polytopes
| dc.creator | Kamnitzer, Joel | |
| dc.date | 2005-05-18 | |
| dc.date | 2006-01-09 | |
| dc.date.accessioned | 2026-07-07T06:39:59Z | |
| dc.date.available | 2026-07-07T06:39:59Z | |
| dc.description | In an earlier work, we proved that MV polytopes parameterize both Lusztig's canonical basis and the Mirkovic-Vilonen cycles on the Affine Grassmannian. Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles side). We show that these two crystal structures agree. As an application, we consider a conjecture of Anderson-Mirkovic which describes the BFG crystal structure on the level of MV polytopes. We prove their conjecture for sl_n and give a counterexample for sp_6. Finally we explain how Kashiwara data can be recovered from MV polytopes. | |
| dc.description | 27 pages, v2: section on Kashiwara data added | |
| dc.identifier | https://arxiv.org/abs/math/0505398 | |
| dc.identifier | http://arxiv.org/abs/math/0505398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101286 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | The crystal structure on the set of Mirkovic-Vilonen polytopes | |
| dc.type | text |