Overview of the parabolic positive representations of $mathcal{U}_q(mathfrak{g}_mathbb{R})$ (Recent advances in combinatorial representation theory)

Abstract

We give a simplified overview of the construction of a new family of irreducible representations for split real quantum groups $mathcal{U}_q(mathfrak{g}_mathbb{R})$ known as the parabolic positive representations by truncating the standard positive representations. This corresponds to quantizing the parabolic induction representation.