Inducing modules from the centralizer of the Cartan subalgebra yields non-extremal weight modules, and for Uq(sl(2,C)) this construction recovers the admissible unitary representations of Uq(su(1,1)).
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Non-extremal weight modules for quantized universal enveloping algebras
Inducing modules from the centralizer of the Cartan subalgebra yields non-extremal weight modules, and for Uq(sl(2,C)) this construction recovers the admissible unitary representations of Uq(su(1,1)).