JournalsjncgVol. 15, No. 1pp. 79–111

Equivariant vector bundles over quantum spheres

  • Andrey Mudrov

    University of Leicester, UK
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Abstract

We quantize SO(2n+1)SO(2n+1)-equivariant vector bundles over an even complex sphere S2n\mathbb{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 Sq2n\mathbb{S}^{2n}_q and prove their complete reducibility.

Cite this article

Andrey Mudrov, Equivariant vector bundles over quantum spheres. J. Noncommut. Geom. 15 (2021), no. 1, pp. 79–111

DOI 10.4171/JNCG/396