  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}.
