Nonclassical type representations of the q-deformed algebra U '(q)(so(n))

The nonstandard q-deformation U-q'(so(n)) of the universal enveloping algeb ra U(so(n)) has irreducible finite dimensional representations which ara a q-deformation of the well-known irreducible finite dimensional representati ons of U(so(n)). But U-q'(so(n)) also has irreducible finite dimensional re presentations which have no classical analogue. The aim of this paper is to give these representations which are called nonclassical type representati ons. They are given by explicit formulas for operators of the representatio ns corresponding to the generators of U-q'(so(n)).