Crystal bases of the Fock space representations and string functions
| dc.creator | Kang, Seok-Jin | |
| dc.creator | Kwon, Jae-Hoon | |
| dc.date | 2004-03-05 | |
| dc.date.accessioned | 2026-07-07T05:06:08Z | |
| dc.date.available | 2026-07-07T05:06:08Z | |
| dc.description | Let $U_q(\frak{g})$ a the quantum affine algebra of type $A_n^{(1)}$, $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_n^{(1)}$, $D_n^{(1)}$ and $D_{n+1}^{(2)}$, and let $\mathcal{F}(Λ)$ be the Fock space representation for a level 1 dominant integral weight $Λ$. Using the crystal basis of $\mathcal{F}(Λ)$ and its characterization in terms of abacus, we construct an explicit bijection between the set of weight vectors in $\mathcal{F}(Λ)_{λ-mδ}$ ($m\geq 0$) for a maximal weight $λ$ and the set of certain ordered sequences of partitions. As a corollary, we obtain the string function of the basic representation $V(Λ)$. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403105 | |
| dc.identifier | http://arxiv.org/abs/math/0403105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70368 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B37 | |
| dc.title | Crystal bases of the Fock space representations and string functions | |
| dc.type | text |