Integrable defects in affine Toda field theory and infinite-dimensional representations of quantum groups

Abstract Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang–Baxter equations, and second by solving a linear intertwining relation between a finite-dimensional representation of the relevant Borel subalgebra of the quantum group underpinning the integrable quantum field theory and a particular infinite-dimensional representation expressed in terms of sets of generalised ‘quantum’ annihilation and creation operators. The principal examples analysed are based on the a 2 ( 2 ) and a n ( 1 ) affine Toda models but examples of similar infinite-dimensional representations for quantum Borel algebras for all other affine Toda theories are also provided.