  The problem of resonant transport of strongly interacting electrons through a
one-dimensional single-level vibrating quantum dot is being considered. In this
paper, we generalize the Komnik and Gogolin model [Phys. Rev. Lett., 90,
246403, (2003)] for the single-electron transistor with g=1/2 Luttinger liquid
leads to the case of a strong electron-vibron interaction in a quantum dot. The
effective transmission coefficient and differential conductance of the system
has been derived for the general case of asymmetric tunnel barriers. The main
result obtained is that, in the zero-temperature limit, the resonant
polaron-assisted tunneling with perfect transmission is possible. This resonant
tunneling is of the novel (Andreev-like) type due to a special
electron-electron interaction in the leads. As a result, a strong domination of
resonant polaron-assisted electron transport at low temperatures has been
found. Additional narrowing due to electron-electron interaction in the leads,
is roughly the same for all polaron-assisted resonances.
