q-deformed Coxeter element in Non-simply-laced Affine Toda Field Theories

Details q-deformed Coxeter element in Non-simply-laced Affine Toda Field Theories q-deformed Coxeter element in Non-simply-laced Affine Toda Field Theories

1997-06-09

arxiv.org/abs/hep-th/9706054v1

Nucl.Phys. B504 (1997) 738-752

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, latex, no figures

Scientific paper

The Lie algebraic structures of the S-matrices for the affine Toda field theories based on the dual pairs (X_N^{(1)}, Y_M^{(l)}) are discussed. For the non-simply-laced horizontal subalgebra X_N and the simply-laced horizontal subalgebra Y_M, 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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