  In this work we investigate the possibility of using the reflection algebra
as a source of functional equations. More precisely, we obtain functional
relations determining the partition function of the six-vertex model with
domain-wall boundary conditions and one reflecting end. The model's partition
function is expressed as a multiple-contour integral that allows the
homogeneous limit to be obtained straightforwardly. Our functional equations
are also shown to give rise to a consistent set of partial differential
equations for the partition function.
