Rational R - matrices , centralizer algebras and tensor identities for e 6 and e 7 families of Lie algebras
نویسندگان
چکیده
We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s 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 e7 and e6 on their lowest-dimensional representations and (up to three-fold) tensor products thereof, giving bases for them and a number of identities satisfied by the algebras’ defining invariant tensors. [email protected] [email protected]
منابع مشابه
2 4 N ov 2 00 7 Rational R - matrices , centralizer algebras and tensor identities for e 6 and e 7 exceptional families of Lie algebras
We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s 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 e7 and e6 on their lowest-dimension...
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We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s 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 e7 and e6 on their lowest-dimension...
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