We quantize $SO(2n+1)$-equivariant 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 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 $\mathbb{S}^{2n}_q$ and prove their complete reducibility.

中文翻译：

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量子球上的等变向量束

我们将偶数复杂球面$ \ mathbb {S} ^ {2n} $上的$ SO（2n + 1）$-等变矢量束量化为其量化坐标环上的单面射影模块。我们以两种不同的方式实现它们：作为伪抛物线模块之间的线性映射以及作为正交量子组的感应模块。基于此替代方案，我们研究与$ \ mathbb {S} ^ {2n} _q $相关的量子对称对的表示，并证明它们的完全可约性。