Equivariant vector bundles over even quantum spheres

摘要

We quantize SO(2n + 1)-equivariant vector bundles on an even complex sphere S-2n as 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 S-q(2n) and prove their complete reducibility.