Physics – Mathematical Physics
Scientific paper
2003-07-08
J.Phys.A36:10551-10572,2003
Physics
Mathematical Physics
24 pages, LaTeX using IOP styles, many figures included; typo in formula (7) corrected
Scientific paper
10.1088/0305-4470/36/42/010
We define new diagram algebras providing a sequence of multiparameter generalisations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional Statistical Mechanics. These algebras give a rigorous foundation to the various "multi-colour algebras" of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in Statistical Mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations.
Grimm Uwe
Martin Paul P.
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