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We quantize -equivariant vector bundles over an even complex sphere 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 and prove their complete reducibility.
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Andrey Mudrov, Equivariant vector bundles over quantum spheres. J. Noncommut. Geom. 15 (2021), no. 1, pp. 79–111DOI 10.4171/JNCG/396