On the quantum flag manifold $S{U}_q(3)/{\mathbb{T}}^2$

Abstract

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

11 pages; to appear in the proceedings of XXXVI Workshop on Geometric Methods in Physics, Białowieża 2018; v2 two references added