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

Harold Steinacker

doi:10.1007/s002200050315

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arXiv · q-alg/9611009

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

Harold Steinacker

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Abstract

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 $q = e^{i π/M}$, 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 $q = e^{iπ/M}$.

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BibTeX RIS

Harold Steinacker. 1997-08-02. Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity. https://doi.org/10.1007/s002200050315

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