  We study the one-dimensional Fermionic Hubbard model with SU(N) spin symmetry
in the incommensurate filling case. The basic properties of Green's function,
momentum distribution and tunneling density of states of the system at low
temperature are studied in the frame work of Luttinger liquid theory combined
with Bethe Ansatz solutions for arbitrary interaction. In the strong
interacting case, the system enters the spin-incoherent regime at intermediate
temperature Espin < T < Ec and we obtain the Green's function and tunneling
density of states by generalizing the path integral approach for the SU(2) case
to the SU(N) case in this regime. The theoretical results we obtained agree
qualitatively with the experiments on the one-dimensional alkaline earth atomic
system with SU(N) spin symmetry. The similarities and difference between the
one-dimensional SU(N) Fermionic Hubbard system at large N and the
one-dimensional spinless Bosonic system are also investigated.
