  We discuss the conductance of a Luttinger liquid interrupted by a quantum dot
containing a single resonant level. Using bosonisation and re-fermionisation
methods, we find a mapping to a Kondo-type problem which possesses a
non-trivial Toulouse-type solvable point. At this point, we obtain an analytic
expression for the non-linear current-voltage characteristics and analyse the
differential conductance and the width of the resonance peak as functions of
bias and gate voltages, temperature, and barrier asymmetry. We also determine
the exact scaling function for the linear conductance.
