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)).
Generalized Verma modules over U_q(sl_n(C))
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We construct realizations of quantum generalized Verma modules for U_q(sl_n(C)) by quan- tum differential operators. Taking the classical limit q ! 1 provides a realization of classical generalized Verma modules for sl_n(C) by differential operators.
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math.QA 1years
2019 1verdicts
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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)).