  We study point contact tunneling between two leads of a Tomonaga-Luttinger
liquid through two degenerate resonant levels in parallel. This is one of the
simplest cases of a quantum junction problem where the Fermi statistics of the
electrons plays a non-trivial role through the Klein factors appearing in
bosonization. Using a mapping to a `generalized Coulomb model' studied in the
context of the dissipative Hofstadter model, we find that any asymmetry in the
tunneling amplitudes from the two leads grows at low temperatures, so that
ultimately there is no conductance across the system. For the symmetric case,
we identify a non-trivial fixed point of this model; the conductance at that
point is generally different from the conductance through a single resonant
level.
