Abstract
We describe the action of the center of the quantum group Uq (𝔤) on the tensor product V ⊗ L(λ) of an infinite-dimensional representation V having an infinitesimal character χτ and an irreducible finite-dimensional Uq (𝔤) representation L(λ) of highest weight λ. We apply this result in order to describe the tensor product of a Whittaker module and a finite-dimensional simple module for the algebra Uq(𝔰l2).
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