Quantum Group Symmetry in sine-Gordon and Affine Toda Field Theories on the Half-Line

 We 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 U _q (ĝ). Received: 10 December 2001 / Accepted: 7 October 2002 Published online: 19 December 2002