A vector partition function for the multiplicities of sl_k(C)
| dc.creator | Billey, Sara | |
| dc.creator | Guillemin, Victor | |
| dc.creator | Rassart, Etienne | |
| dc.date | 2003-07-16 | |
| dc.date.accessioned | 2026-07-07T04:59:42Z | |
| dc.date.available | 2026-07-07T04:59:42Z | |
| dc.description | We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply known results about partition functions to derive interesting properties of the weight diagrams. We relate this description to that of the Duistermaat-Heckman measure from symplectic geometry, which gives a large-scale limit way to look at multiplicity diagrams. We also provide an explanation for why the weight polynomials in the boundary regions of the weight diagrams exhibit a number of linear factors. Using symplectic geometry, we prove that the partition of the permutahedron into domains of polynomiality of the Duistermaat-Heckman function is the same as that for the weight multiplicity function, and give an elementary proof of this for sl_4(C) (A_3). | |
| dc.description | 34 pages, 11 figures and diagrams; submitted to Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0307227 | |
| dc.identifier | http://arxiv.org/abs/math/0307227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68093 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 05E15 (Primary); 52B20, 53D20, 68W30 (Secondary) | |
| dc.title | A vector partition function for the multiplicities of sl_k(C) | |
| dc.type | text |