  The Haldane pseudopotential construction has been an extremely powerful
concept in quantum Hall physics --- it not only gives a minimal description of
the space of Hamiltonians but also suggests special model Hamiltonians (those
where certain pseudopotential are set to zero) that may have exactly solvable
ground states with interesting properties. The purpose of this paper is to
generalize the pseudopotential construction to situations where interactions
are N-body and where the particles may have internal degrees of freedom such as
spin or valley index. Assuming a rotationally invariant Hamiltonian, the
essence of the problem is to obtain a full basis of wavefunctions for N
particles with fixed relative angular momentum L. This basis decomposes into
representations of SU(n) with n the number of internal degrees of freedom. We
give special attention to the case where the internal degree of freedom has n=2
states, which encompasses the important cases of spin-1/2 particles and quantum
Hall bilayers. We also discuss in some detail the cases of spin-1 particles
(n=3) and graphene (n=4, including two spin and two valley degrees of freedom).
