  We show that the problem of impurity tunneling in a Luttinger liquid of
electrons with spin is solvable in the spin isotropic case ($g_\sigma=2$,
$g_\rho$ arbitrary). The resulting integrable model is similar to a two channel
anisotropic Kondo model, but with the impurity spin in a "cyclic
representation" of the quantum algebra $su(2)_q$ associated with the
anisotropy. Using exact, non-perturbative techniques we study the RG flow, and
compute the DC conductance. As expected from the analysis of Kane and Fisher we
find that the IR fixed point corresponds to two separate leads. We also prove
an exact duality between the UV and IR expansions of the current at vanishing
temperature.
