Crystal bases of the Fock space representations and string functions

dc.creatorKang, Seok-Jin
dc.creatorKwon, Jae-Hoon
dc.date2004-03-05
dc.date.accessioned2026-07-07T05:06:08Z
dc.date.available2026-07-07T05:06:08Z
dc.descriptionLet $U_q(\frak{g})$ 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.description31 pages
dc.identifierhttps://arxiv.org/abs/math/0403105
dc.identifierhttp://arxiv.org/abs/math/0403105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70368
dc.subjectQuantum Algebra
dc.subject17B37
dc.titleCrystal bases of the Fock space representations and string functions
dc.typetext

Files

Collections