Representations of $SO(5{)}_q$ and Non-Minimal $q$-Deformation

Abstract

Representations of $SO(5{)}_q$ can be constructed on bases such that either the Chevalley triplet $(e_1,f_1,h_1)$ or $(e_2,f_2,h_2)$ has the standard $SU(2{)}_q$ matrix elements. The other triplet in each cases has a more complicated action. The $q$-deformation of such representations present striking differences. In one case a {\bf non-minimal} deformation is found to be essential. This is explained and illustrated below. Broader interests of a parallel use of the two bases are pointed out.

arXiv comment11 pages, Tex.file

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