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Yangians, integrable quantum systems and Dorey's rule

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Abstract

It was pointed out by P. Dorey that the three-point couplings between the quantum particles in affine Toda field theories have a remarkable Lie-theoretic interpretation. It is also well known that such theories admit quantum affine algebras as “quantum symmetry groups,” and widely believed that the quantum particles correspond to the so-called fundamental representations of these algebras. This led to the conjecture that Dorey's rule should describe when a fundamental representation occurs with non-zero multiplicity in a tensor product of two other fundamental representations. The purpose of this paper is to prove this conjecture, both for quantum affine algebras and for Yangians. The result reveals a hitherto unsuspected role played by Coxeter elements (and their twisted analogues) in the representation theory of these algebras.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92521, Riverside, CA, USA

    Vyjayanthi Chari

  2. Department of Mathematics, King's College, Strand, WC2R 2LS, London, UK

    Andrew Pressley

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  1. Vyjayanthi Chari
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  2. Andrew Pressley
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Communicated by M. Jimbo

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Chari, V., Pressley, A. Yangians, integrable quantum systems and Dorey's rule. Commun.Math. Phys. 181, 265–302 (1996). https://doi.org/10.1007/BF02101006

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