  We investigate a system of multiple Majorana states at the end of a
topological superconducting wire coupled to a normal lead. For a minimum of
three Majorana fermions at the interface, we find nontrivial renormalization
physics. Interface tunneling processes can be classified in terms of spin-1/2
and spin-3/2 irreducible representations of the SU(2) group. We show that the
renormalization of the tunneling amplitudes belonging to different
representations is completely different in that one type is suppressed, whereas
the other is enhanced, depending on the sign of the interaction coupling. This
results in distinct temperature dependencies of the tunneling current through
the interface and different spin polarizations of this current.
