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

Let be the quantum affine algebra associated to a simply-laced simple Lie algebra . We examine the relationship between Dorey’s rule, which is a geometrical statement about Coxeter orbits of -weights, and the structure of q -characters of fundamental representations V i , a of . 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 .