Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems $B_{n},C_{n}$ and $D_{n}.$
| dc.creator | Lecouvey, Cedric | |
| dc.date | 2004-06-28 | |
| dc.date.accessioned | 2026-07-07T05:09:46Z | |
| dc.date.available | 2026-07-07T05:09:46Z | |
| dc.description | We use Kashiwara-Nakashima's combinatorics of crystal graphs associated to the roots sytems $B_{n}$ and $D_{n}$ to extend the results of \QCITE{cite}{}{lec3} and \QCITE{cite}{}{Mor} by showing that Morris type recurrence formulas also exist for the orthogonal root systems. We derive from these formulas a statistic on Kashiwara-Nakashima's tableaux of types $B_{n},C_{n}$ and $D_{n}$ generalizing Lascoux-Sch\UNICODE{0xfc}tzenberger's charge and from which it is possible to compute the Kostka-Foulkes polynomials $K_{λ,μ}(q)$ with restrictive conditions on $(λ,μ)$ . This statistic is different from that obtained in \QCITE{cite}{}{lec3} from the cyclage graph structure on tableaux of type $C_{n}$. We show that such a structure also exists for the tableaux of types $B_{n}$ and $D_{n}$ but can not be simply related to the Kostka-Foulkes polynomials. Finally we give explicit formulas for $K_{λ,μ}(q)$ when $| λ| \leq 3,$ or $n=2$ and $μ=0$. | |
| dc.identifier | https://arxiv.org/abs/math/0406574 | |
| dc.identifier | http://arxiv.org/abs/math/0406574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71708 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems $B_{n},C_{n}$ and $D_{n}.$ | |
| dc.type | text |