$SO(5)_{q}$ and Contraction

Details $SO(5)_{q}$ and Contraction $SO(5)_{q}$ and Contraction

1994-05-26

arxiv.org/abs/hep-th/9405165v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages Tex, written version of a talk presented at XXX Karpacz Winter school

Scientific paper

Representations of $SO(5)_{q}$ are constructed explicitly on the Chevalley basis for all $q$, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal number being 4. A prescription for contraction is given such that a complete Hopf algebra is immediately obtained for the non-semisimple contracted case. For $q$ a root of unity the periodic representations for $SO(5)_{q}$ and the contracted algebra are obtained directly in the "fractional part" formalism which unifies the treatments for the generic and root of unity cases. The $q$-deformed quadratic Casimir operator is explicitly evaluated for the representations presented.

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