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Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

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Abstract

Let \({U_q(\widehat{\mathfrak g})}\) be the quantum affine algebra associated to a simply-laced simple Lie algebra \({\mathfrak{g}}\) . We examine the relationship between Dorey’s rule, which is a geometrical statement about Coxeter orbits of \({\mathfrak{g}}\) -weights, and the structure of q-characters of fundamental representations V i,a of \({U_q(\widehat{\mathfrak g})}\) . In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product \({V_{i,a}\otimes V_{j,b}\otimes V_{k,c}}\) .

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    C. A. S. Young

  2. Laboratoire de Physique Théorique, Université Paris-Sud 11/CNRS, 91405, Orsay Cedex, France

    R. Zegers

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  1. C. A. S. Young
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  2. R. Zegers
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Correspondence to C. A. S. Young.

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Communicated by Y. Kawahigashi

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Young, C.A.S., Zegers, R. Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras. Commun. Math. Phys. 302, 789–813 (2011). https://doi.org/10.1007/s00220-011-1189-x

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