  Employing an inhomogeneous solvable lattice model, we derive an exact
expression for a boundary-to-boundary edge current on a lattice of finite
width. This current is an example of a class of parafermionic observables
recently introduced in an attempt to rigorously prove conformal invariance of
the scaling limit of critical two-dimensional lattice models. It also
corresponds to the spin current at the spin-Quantum Hall transition in a model
introduced by Chalker and Coddington, and generalized by Gruzberg, Ludwig and
Read. Our result is derived from a solution of the $q$-deformed
Knizhnik-Zamolodchikov equation, and is expressed in terms of a symplectic
Toda-lattice wave-function.
