TY - JOUR

T1 - Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

AU - Young, Charles A. S.

AU - Zegers, R.

PY - 2011

Y1 - 2011

N2 - 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}

AB - 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}

KW - math.QA

UR - http://www.scopus.com/inward/record.url?scp=79951855374&partnerID=8YFLogxK

U2 - 10.1007/s00220-011-1189-x

DO - 10.1007/s00220-011-1189-x

M3 - Article

SN - 1432-0916

VL - 302

SP - 789

EP - 813

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -