  The linear response transport properties of carbon nanotube quantum dot in
the strongly correlated regime are discussed. The finite-U mean field slave
boson approach is used to study many-body effects. Magnetic field can rebuilt
Kondo correlations, which are destroyed by the effect of spin-orbit interaction
or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects
of different types: spin, valley or spin-valley, also more exotic phenomena
appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the
effective intervalley exchange induced by short-range part of Coulomb
interaction or due to the intershell mixing. In narrow gap nanotubes the full
spin-orbital degeneracy might be recovered in the absence of magnetic field
opening the condition for a formation of SU(4) Kondo resonance.
