  In this work we study a system of interacting fermions with large spin and
SP(N) symmetry. We contrast their behaviour with the case of SU(N) symmetry by
analysing the conserved quantities and the dynamics in each case. We also
develop the Fermi liquid theory for fermions with SP(N) symmetry. We find that
the effective mass and inverse compressibility are always enhanced in the
presence of interactions, and that the N-dependence of the enhancement is
qualitatively different in distinct parameter regimes. The Wilson ratio can be
enhanced, indicating that the system can be made closer to a magnetic
instability, in contrast to the SU(N) scenario. We conclude discussing what are
the experimental routes to SP(N) symmetry within cold atoms and the exciting
possibility to realize physics in higher dimensions in these systems.
