The principal indecomposable modules of the dilute Temperley-Lieb algebra
نویسندگان
چکیده
منابع مشابه
The two-boundary Temperley-Lieb algebra
We study a two-boundary extension of the Temperley-Lieb algebra which has recently arisen in statistical mechanics. This algebra lies in a quotient of the affine Hecke algebra of type C and has a natural diagrammatic representation. The algebra has three parameters and, for generic values of these, we determine its representation theory. We use the action of the centre of the affine Hecke algeb...
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The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram deter...
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The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley–Lieb algebra which is an extension of the Temperley–Lieb algebra by adding the group algebra of the symmetrical group. We make a connection clear between the Brauer algebra and...
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In this paper, we solve a problem posed by the late Rodica Simion regarding type B Gram determinants, cf. [5]. We present this in a fashion influenced by the work of W.B.R.Lickorish on Witten-Reshetikhin-Turaev invariants of 3-manifolds. We will give a history of this problem in a sequel paper in which we also plan to address other related questions by Simion [6, 5] and connect the problem to F...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2014
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4901546