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Rational R-matrices, centralizer algebras and tensor identities for e6 and e7 exceptional families of Lie algebras

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JournalJournal of Mathematical Physics
DatePublished - Oct 2007
Issue number10
Volume48
Number of pages14
Pages (from-to)Art. No. 103507
Original languageEnglish

Abstract

We use Cvitanovic's [Group Theory (Princeton University Press, Princeton, NJ, in press) (http://www.nbi.dk/GroupTheory/); Phys. Rev. D 14, 1536 (1976)] diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation [Yang-Baxter Equation in Integrable Systems, edited by M. Jimbo, Advanced Series in Mathematical Physics Vol. 10 (World scientific, Singapore, 1990)] associated with the e(6) and e(7) families of Lie algebras, and thus explain Westbury's [J. Phys. A 36, 2857 (2003)] observations about their uniform spectral decompositions. In doing so, we explore the extensions of the Brauer and symmetric group algebras to the centralizer algebras of e(7) and e(6) on their lowest-dimensional representations and (up to threefold) tensor products thereof, giving bases for them and a range of identities satisfied by the algebras' defining invariant tensors. (C) 2007 American Institute of Physics.

    Research areas

  • FACTORIZED S-MATRICES, 2 DIMENSIONS, MODELS, REPRESENTATIONS, DIAGRAMS

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