Left Regular Representation of $sl_q(3)$: Reduction and Intertwiners

TL;DR

This paper investigates the reduction of the left regular representation of the quantum algebra $sl_q(3)$ and constructs $q$-difference intertwining operators, linking irreducible representations to line bundles over the q-flag manifold.

Contribution

It introduces explicit $q$-difference intertwining operators for $sl_q(3)$ and connects irreducible representations to geometric structures on the q-flag manifold.

Findings

Construction of $q$-difference intertwining operators.

Identification of irreducible representations with line bundles.

Analysis of the reduction process of the regular representation.

Abstract

Reduction of the left regular representation of quantum algebra $sl_q(3)$ is studied and ~$q$-difference intertwining operators are constructed. The irreducible representations correspond to the spaces of local sections of certain line bundles over the q-flag manifold.