The embedding U-q '(so(3)) subset of U-q(sl(3))

We study the embedding U-q'(so(3)) subset of U-q(sl(3)), where U-q(sl(3)) i s a well known Drinfeld-Jimbo quantum algebra and the algebra U-q'(so(3)) i s the cyclically symmetric q-deformation of the universal enveloping algebr a U (so(3)) of the Lie algebra sos which is not a Drinfeld-Jimbo quantum al gebra. Finite-dimensional irreducible representations of U-q(sl(3)) are dec omposed into irreducible representations of U-q'(So(3)) An explicit express ion for the matrix of the transition from the Gel'fand-Tsetlin basis for U- q(sl(3)) to the bases of irreducible representations of U-q'(so(3)) is calc ulated for representations of U-q(sl(3)) With highest weights (l, 0, 0). En tries of this matrix are expressed in terms of products of dual q-Krawtchou k polynomials and dual q-Hahn polynomials. Expressions for representation o perators of U-q(sl(3)) in the U-q'(so(3)) basis are given.