Finite Dimensional Unitary Representations of Quantum Anti–de Sitter Groups at Roots of Unity |
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Authors: | Harold Steinacker |
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Affiliation: | Theoretical Physics Group, Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA and Department of Physics, University of California, Berkeley, California 94720, USA.? E-mail: hsteinac@physics.berkeley.edu, US
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Abstract: | We study irreducible unitary representations 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 representations corresponding to all classical one-particle representations with integral weights are found for , 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 . Received: 27 November 1996 / Accepted: 28 July 1997 |
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