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

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

2009-10-23

arxiv.org/abs/0910.4477v2

Commun.Math.Phys.302:789-813,2011

Mathematics

Quantum Algebra

30 pages, latex; v2, to appear in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-011-1189-x

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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