Grimm, Uwe and Martin, Paul P.
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|DOI (Digital Object Identifier) Link:||http://doi.org/10.1088/0305-4470/36/42/010|
|Google Scholar:||Look up in Google Scholar|
We define new diagram algebras providing a sequence of multiparameter generalizations 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.
|Item Type:||Journal Article|
|Extra Information:||Preprint version math-ph/0307017 available at http://arxiv.org/abs/math-ph/0307017|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Uwe Grimm|
|Date Deposited:||07 Jun 2006|
|Last Modified:||23 Feb 2016 18:13|
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