  Through Haldane's construction, the fractional quantum Hall states on a
two-sphere was shown to be the ground states of {\it one-dimensional} SU(2)
spin Hamiltonians. In this Letter we generalize this construction to obtain a
new class of SU(N) spin Hamiltonians. These Hamiltonians describes
center-of-mass-position conserving pair hopping fermions in space dimension
$d\ge 2$. We conjecture that the excitations of these models posses fractional
fermion number.
