Raising/lowering maps and modules for the quantum affine algebra $U_q(sl_2hat)$

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dc.creatorFunk-Neubauer, Darren
dc.date2005-06-30
dc.date2006-07-31
dc.date.accessioned2026-07-07T09:39:45Z
dc.date.available2026-07-07T09:39:45Z
dc.descriptionLet V denote a finite dimensional vector space over an algebraically closed field. Let U_0, U_1,..., U_d denote a sequence of nonzero subspaces whose direct sum is V. Let R:V \to V and L:V \to V denote linear maps with the following properties: for 0 \leq i \leq d, R U_i \subseteq U_{i+1} and L U_i \subseteq U_{i-1} where U_{-1}=0, U_{d+1}=0; for 0 \leq i \leq d/2, the restrictions R^{d-2i}: U_i \to U_{d-i} and L^{d-2i}: U_{d-i} \to U_i are bijections; the maps R and L satisfy the cubic q-Serre relations where q is nonzero and not a root of unity. Let K:V \to V be the linear map such that (K-q^{2i-d}I)U_i=0 for 0 \leq i \leq d. We show that there exists a unique U_q(sl_2hat)-module structure on V such that each of R-e^{-}_1, L-e^{-}_0, K-K_0, and K^{-1}-K_1 vanish on V, where e^{-}_1, e^{-}_0, K_0, K_1 are Chevalley generators for U_q(sl_2hat). We determine which U_q(sl_2hat)-modules arise from our construction.
dc.description21 pages, to be published in Communications in Algebra, longer introduction added, some proofs shortened, and some notation changes
dc.identifierhttps://arxiv.org/abs/math/0506629
dc.identifierhttp://arxiv.org/abs/math/0506629
dc.identifierCommunications in Algebra, vol. 35, #7 (2007), 2140--2159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161287
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleRaising/lowering maps and modules for the quantum affine algebra $U_q(sl_2hat)$
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