Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
Copyright policy )Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
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}.
30 pages, latex; v2, to appear in Communications in Mathematical Physics
High Energy Physics - Theory, [MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], q-characters, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Dorey's rule, simply-laced quantum affine algebras, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Quantum groups and related algebraic methods applied to problems in quantum theory
High Energy Physics - Theory, [MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], q-characters, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Dorey's rule, simply-laced quantum affine algebras, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Quantum groups and related algebraic methods applied to problems in quantum theory
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