2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137678We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining property for representations of certain coideal subalgebras of quantized affine algebras.AMSLatex, 20 pages. Typos corrected and reference added. To appear in Commun. Math. PhysHigh Energy Physics - TheoryQuantum Algebratext