Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure

Let g be a compact simple Lie algebra. We modify the quantized enveloping *-algebra associated to g by a real-valued character on the positive part of the root lattice. We study the ensuing Verma module theory, and the associated quotients of these modified quantized enveloping *-algebras. Restricting to the locally finite part by means of a natural adjoint action, we obtain in particular examples of quantum homogeneous spaces in the operator algebraic setting.

Keywords:quantized enveloping algebras