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Transmission matrices for two types of integrable defect are calculatedexplicitly, first by solving directly the nonlinear transmission Yang-Baxterequations, and second by solving a linear intertwining relation between afinite dimensional representation of the relevant Borel subalgebra of thequantum group underpinning the integrable quantum field theory and a particularinfinite dimensional representation expressed in terms of sets of generalized`quantum' annihilation and creation operators. The principal examples analysedare based on the $a_2^{(2)}$ and $a_n^{(1)}$ affine Toda models but examples ofsimilar infinite dimensional representations for quantum Borel algebras for allother affine Toda theories are also provided.

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