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

TL;DR

This paper introduces q- and p-deformations of Coxeter elements to analyze the Lie algebraic structures of S-matrices in affine Toda field theories, revealing new algebraic relations and generalizations of Dorey's rule.

Contribution

It presents a novel q-deformation of Coxeter elements for non-simply-laced algebras and connects these to S-matrix structures and generalized Dorey's rule.

Findings

Derived generating functions for S-matrix building blocks.

Established relations between deformed Coxeter elements and Dorey's rule.

Provided algebraic expressions for multiplicities in affine Toda theories.

Abstract

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.