q-deformed Coxeter element in Non-simply-laced Affine Toda Field Theories
Abstract
The Lie algebraic structures of the S-matrices for the affine Toda field theories based on the dual pairs (XN(1), YM(l)) are discussed. For the non-simply-laced horizontal subalgebra XN and the simply-laced horizontal subalgebra YM, we introduce a ``q-deformation'' of a Coxeter element and a ``p-deformation'' of a twisted Coxeter element respectively. Using these deformed objects, expressions for the generating function of the multiplicities of the building block of the S-matrices are obtained. The relation between the deformed version of Dorey's rule and generalized Dorey's rule due to Chari and Pressley are discussed.
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