Equivariant vector bundles over quantum spheres
Copyright policy )Equivariant vector bundles over quantum spheres
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.
equivariant vectorbundles, Deformation quantization, star products, quantum groups, projective modules, quantum sphere, quantum spheres, Quantum groups (quantized enveloping algebras) and related deformations, symmetric pairs, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups and related algebraic methods applied to problems in quantum theory
equivariant vectorbundles, Deformation quantization, star products, quantum groups, projective modules, quantum sphere, quantum spheres, Quantum groups (quantized enveloping algebras) and related deformations, symmetric pairs, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups and related algebraic methods applied to problems in quantum theory
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