Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure

Abstract

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

• compact quantum homogeneous spaces; quantized universal enveloping algebras; Hopf-Galois theory; Verma modules