  We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for
$q$ a root of unity, which are finite dimensional. Among others, unitary \reps
corresponding to all classical one-particle representations with integral
weights are found for $q = e^{i \pi /M}$, with $M$ being large enough. In the
"massless" case with spin bigger than or equal to 1 in 4 dimensions, they are
unitarizable only after factoring out a subspace of "pure gauges", as
classically. A truncated associative tensor product describing unitary
many-particle representations is defined for $q = e^{i\pi /M}$.
