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The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation U′q(son) (which does not coincide with the Drinfel'd-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son(ℂ)) of the Lie algebra son(ℂ) when q is not a root of unity. These representations are exhausted by irreducible representations of the classical type and of the nonclassical type. The theorem on complete reducibility of finite-dimensional representations of U′q(son) is proved.

international journal of mathematics and mathematical sciences

Classification theorem on irreducible representations of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$q$" id="E1"><mml:mi>q</mml:mi></mml:math>-deformed algebra<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$u'_{q}({\mathrm{so}}_{n})$" id="E2"><mml:msub><mml:msup><mml:mi>U</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi>q</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>so</mml:mtext></mml:mrow><mml:mi>n</mml:mi></…

Classification theorem on irreducible representations of theq-deformed algebraU′q(son