On the quantum flag manifold \({{SU}_{q}} (3)/{\mathbb{T}^2}\)

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” \( \mathbb{C}{{P}^1_q} \rightarrow {SU_q}(3)/\mathbb{T}^2 \rightarrow \mathbb{C}{{P}^2_q}\) .