  The duality principle for Gabor frames states that a Gabor sequence obtained
by a time-frequency lattice is a frame for $L^{2}(\R^{d})$ if and only if the
associated adjoint Gabor sequence is a Riesz sequence. We prove that this
duality principle extends to any dual pairs of projective unitary
representations of countable groups. We examine the existence problem of dual
pairs and establish some connection with classification problems for $\rm
II_{1}$ factors. While in general such a pair may not exist for some groups, we
show that such a dual pair always exists for every subrepresentation of the
left regular unitary representation when $G$ is an abelian infinite countable
group or an amenable ICC group. For free groups with finitely many generators,
the existence problem of such a dual pair is equivalent to the well known
problem about the classification of free group von Neumann algebras.
