Abstract
We construct two examples of q-deformed classical Howe dual pairs (sl(2,C),so(3,C)) and (sl(2,C),sl(n,C)). Moreover, we obtain a noncommutative version of the first fundamental theorem of classical invariant theory. Our approach to these dualities differs from [9] and [11]. Furthermore, we solve the tensor product decomposition problem for Verma modules over Uq(sl(2,C)) provided q is not a root of unity.
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