q-deformed Coxeter element in non-simply laced affine Toda field theories Original Research Article

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 Doreyʹs rule and the generalized Doreyʹs rule due to Chari and Pressley are discussed.