# On the quantum flag manifold $SU_q(3)/\mathbb{T}^2$

## TL;DR

This paper investigates the structure of the $C^*$-algebra of functions on the quantum flag manifold $SU_q(3)/\mathbb{T}^2$, analyzing its representations and primitive ideals to understand its geometric and algebraic properties.

## Contribution

It provides a detailed analysis of the irreducible representations and primitive ideal space of the quantum flag manifold $SU_q(3)/\mathbb{T}^2$, advancing understanding of its quantum geometric structure.

## Key findings

- Characterization of irreducible representations
- Description of the primitive ideal space
- Insights into the quantum sphere bundle structure

## Abstract

The structure of the $C^*$-algebra of functions on the quantum flag manifold $SU_q(3)/\mathbb{T}^2$ is investigated. Building on the representation theory of $C(SU_q(3))$, we analyze irreducible representations and the primitive ideal space of $C(SU_q(3)/\mathbb{T}^2)$, with a view towards unearthing the `quantum sphere bundle' $\mathbb{C} P_q^1 \to SU_q(3)/\mathbb{T}^2 \to \mathbb{C} P_q^2$