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

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

1996-11-08

arxiv.org/abs/q-alg/9611009v3

Commun.Math.Phys. 192 (1998) 687-706

Physics

High Energy Physics

High Energy Physics - Theory

More systematic proof of statements on the structure of irreps, some typos corrected. 25 pages LaTeX, 4 figures included using

Scientific paper

10.1007/s002200050315

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 $q = e^{i\pi /M}$.

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