  This is a condensed write-up of a talk delivered at the Ramanujan
International Symposium on Kac-Moody Lie algebras and Applications in Chennai
in January 2002. The talk introduces special coideal subalgebras of quantum
affine algebras which appear in physics when solitons are restricted to live on
a half-line by an integrable boundary condition. We review how the quantum
affine symmetry determines the soliton S-matrix in affine Toda field theory and
then go on to use the unbroken coideal subalgebra on the half-line to determine
the soliton reflection matrix. This gives a representation theoretic method for
the solution of the reflection equation (boundary Yang-Baxter equation) by
reducing it to a linear equation.
