Algebras in higher-dimensional statistical mechanics - the exceptional partition (mean field) algebras |
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| Authors: | Paul Martin Hubert Saleur |
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| Institution: | (1) Mathematics Department, City University, ECIV 0HB London, U.K.;(2) Physics Department and Mathematics Department, University of Southern California, 90089 Los Angeles, CA, USA |
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| Abstract: | We determine the structure of the partition algebraP
n(Q) (a generalized Temperley-Lieb algebra) for specific values ofQ   , focusing on the quotient which gives rise to the partition function ofn siteQ-state Potts models (in the continuousQ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is nonsemisimple iffQ is a nonnegative integer less than 2n-1. We determine the dimension of the key irreducible representation in every specialization.Work supported by the Packard Foundation. |
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| Keywords: | 81R05 82B20 |
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