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The total angular momentum algebra related to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml66" display="inline" overflow="scroll" altimg="si7.gif"><mml:msub><mml:mrow><mml:mi mathvariant="normal">S</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> Dunkl Dirac equation