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arXiv · 1710.05690

Equivariant vector bundles over quantum spheres

Andrey Mudrov
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Abstract

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

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Andrey Mudrov. 2017-10-16. Equivariant vector bundles over quantum spheres. https://arxiv.org/abs/1710.05690

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