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arXiv · 0910.4477

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

C. A. S. Young·R. Zegers
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Abstract

Let Uq(ghat) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey's rule, which is a geometrical statement about Coxeter orbits of g-weights, and the structure of q-characters of fundamental representations V_{i,a} of Uq(ghat). 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} x V_{j,b} x V_{k,c}.

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C. A. S. Young, R. Zegers. 2010-11-02. Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras. https://doi.org/10.1007/s00220-011-1189-x

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