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New Representations of the Temperley-Lieb Algebra with Applications

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Low-Dimensional Topology and Quantum Field Theory

Part of the book series: NATO ASI Series ((NSSB,volume 315))

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Abstract

The Temperley-Lieb algebra, using a new representation in terms of Young tableaux and in conjunction with Bruria Kaufman’s “eigenoperator method”, is applied to obtain new exact results for the Potts model. Cases in which q, the number of colours, is a “Beraha number” can apparently be solved completely. The Young tableaux representation of the Temperley-Lieb algebra is related to the Schensted construction. The connections with B. Kaufman’s “eigenoperator” approach are also discussed.

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Author information

Author notes

  1. H. N. V. Temperley (Emeritus Professor of Applied Mathematics)

    Present address: , Thorney House, Thorney, Langport, Somerset, TA10 0DW, England

Authors and Affiliations

  1. University of Wales, Swansea, USA

    H. N. V. Temperley (Emeritus Professor of Applied Mathematics)

Authors
  1. H. N. V. Temperley
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Editor information

Editors and Affiliations

  1. University of Cambridge, Cambridge, UK

    Hugh Osborn

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© 1993 Springer Science+Business Media New York

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Temperley, H.N.V. (1993). New Representations of the Temperley-Lieb Algebra with Applications. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_18

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  • DOI: https://doi.org/10.1007/978-1-4899-1612-9_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1614-3

  • Online ISBN: 978-1-4899-1612-9

  • eBook Packages: Springer Book Archive

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