Equivariant vector bundles over quantum spheres

We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules its quantized coordinate ring. realize them in two different ways: locally finite $\mathbb{C}$-homs between pseudo-parabolic Verma and induced of the quantum orthogonal group. Based on this alternative, we study representations a symmetric pair related to $\mathbb{S}^{2n}_q$ prove their complete reducibility.