  This contribution to the Proceedings of the Workshop on Integrable Theories,
Solitons and Duality in Sao Paulo in July 2002 summarizes results from the
papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved
charges in the sine-Gordon model and affine Toda field theories on the
half-line. They generate new kinds of symmetry algebras that are coideals of
the usual quantum groups. We show how intertwiners of tensor product
representations of these algebras lead to solutions of the reflection equation.
We describe how this method for finding solutions to the reflection equation
parallels the previously known method of using intertwiners of quantum groups
to find solutions to the Yang-Baxter equation.
