  Understanding the interplay between many-body phenomena and non-equilibrium
in systems with entangled spin and orbital degrees of freedom is a central
objective in nano-electronics. We demonstrate that the combination of Coulomb
interaction, spin-orbit coupling and valley mixing results in a particular
selection of the inelastic virtual processes contributing to the Kondo
resonance in carbon nanotubes at low temperatures. This effect is dictated by
conjugation properties of the underlying carbon nanotube spectrum at zero and
finite magnetic field. Our measurements on a clean carbon nanotube are
complemented by calculations based on a new approach to the non-equilibrium
Kondo problem which well reproduces the rich experimental observations in Kondo
transport.
