A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule

Simple item page
dc.creatorShigechi, Keiichi
dc.creatorUchiyama, Masaru
dc.date2006-12-01
dc.date2007-03-26
dc.date.accessioned2026-07-07T11:03:18Z
dc.date.available2026-07-07T11:03:18Z
dc.descriptionWe study the A_k generalized model of the O(1) loop model on a cylinder. The affine Hecke algebra associated with the model is characterized by a vanishing condition, the cylindric relation. We present two representations of the algebra: the first one is the spin representation, and the other is in the vector space of states of the A_k generalized model. A state of the model is a natural generalization of a link pattern. We propose a new graphical way of dealing with the Yang-Baxter equation and $q$-symmetrizers by the use of the rhombus tiling. The relation between two representations and the meaning of the cylindric relations are clarified. The sum rule for this model is obtained by solving the q-KZ equation at the Razumov-Stroganov point.
dc.description43 pages, 22 figures, LaTeX, (ver 2) Introduction rewritten and Section 4.3 added
dc.identifierhttps://arxiv.org/abs/math-ph/0612001
dc.identifierhttp://arxiv.org/abs/math-ph/0612001
dc.identifierJ.Phys.A40:8923-8958,2007
dc.identifierdoi:10.1088/1751-8113/40/30/019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188546
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subject20C08
dc.titleA_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule
dc.typetext

Files

Collections

arXiv