Equivariant vector bundles over quantum spheres

We quantizeSO(2n+ 1)-equivariant vector bundles on an even complex sphereS2nas one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as linear maps between pseudo-parabolic modules and as induced modules of the orthogonal quantum group. Based on this alternative, we study representations of a quantum symmetric pair related to S2nq and prove their complete reducibility.