The Quantum Flag Manifold $\mathbf{SU_q(3)/\mathbb{T}^2}$ as an Example of a Noncommutative Sphere Bundle

Abstract

The quantum flag manifold ${SU_q(3)/\mathbb{T}^2}$ is interpreted as a noncommutative bundle over the quantum complex projective plane with the quantum or Podle\'s sphere as a fibre. A connection arising from the (associated) quantum principal $U_q(2)$-bundle is described.