Finite – dimensional unitary representations of quantum Anti – de Sitter groups at roots of unity

We study unitary irreducible representations of Uq(SO(2, 1)) and Uq(SO(2, 3)) for q a root of unity, which are finite – dimensional. Among others, unitary representations corresponding to all classical one – particle representations with integral weights are found for q = eiπ/m and m large enough. In the ”massless” case with spin ≥ 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 = eiπ/m. email: [email protected]