  We prove an exact duality between the side-coupled and embedded geometries of
a single level quantum dot attached to a quantum wire in a Luttinger liquid
phase by a tunneling term and interactions. This is valid even in the presence
of a finite bias voltage. Under this relation the Luttinger liquid parameter g
goes into its inverse, and transmittance maps onto reflectance. We then
demonstrate how this duality is revealed by the transport properties of the
side-coupled case. Conductance is found to exhibit an antiresonance as a
function of the level energy, whose width vanishes (enhancing transport) as a
power law for low temperature and bias voltage whenever g>1, and diverges
(suppressing transport) for g<1. On resonance transmission is always destroyed,
unless g is large enough.
