Alcove walks, buildings, symmetric functions and representations
| dc.creator | Parkinson, James | |
| dc.creator | Ram, Arun | |
| dc.date | 2008-07-23 | |
| dc.date.accessioned | 2026-07-07T09:52:19Z | |
| dc.date.available | 2026-07-07T09:52:19Z | |
| dc.description | For a complex simple Lie algebra, the dimension $K_{λμ}$ of the $μ$ weight space of a finite dimensional representation of highest weight $λ$ is the same as the number of Littelmann paths of type $λ$ and weight $μ$. In this paper we give an explicit construction of a path of type $λ$ and weight $μ$ whenever $K_{λμ}\ne 0$. This construction has additional consequences, it produces an explicit point in the building which chamber retracts to $λ$ and sector retracts to $μ$, and an explicit point of the affine Grassmannian in the corresponding Mirković-Vilonen intersection. In an appendix we discuss the connection between retractions in buildings and alcove walks. | |
| dc.identifier | https://arxiv.org/abs/0807.3602 | |
| dc.identifier | http://arxiv.org/abs/0807.3602 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165556 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20G05; 20E42 | |
| dc.title | Alcove walks, buildings, symmetric functions and representations | |
| dc.type | text |