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The representations ofU q(SO4) andU q(SO3,1)

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Summary

We have considered here the (unitary) irreducible representations of theq-deformed algebraU q(SO4) and of theq-deformed Lorentz algebraU q(SO3,1). Both of them contain, as subalgebra, the algebraU q(SO3) which is shown to be isomorphic to the Fairlie-Odesskii algebra. As the list of pairwise nonequivalent irreps of theU q(SO3,1) demonstrates, the set of the parameters, which characterize such irreps is somewhat reduced (due to periodicity properties of the function w(z)=[z]q) in comparison with that of theq=1 (classical) case. From another side, the list of unitary irreps of theU q(SO3,1) contains the strange series which has no classical counterpart (disappears at q=1).

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  1. A. M. Gavrilik
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Published in Teoreticheskaya i Matematicheskaya Fizika. Vol. 95, No. 2, pp. 251–257, May, 1993.

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Gavrilik, A.M. The representations ofU q(SO4) andU q(SO3,1). Theor Math Phys 95, 546–551 (1993). https://doi.org/10.1007/BF01017140

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