Geodesic
Equivariant vector bundles over quantum projective spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 2, pp. 326-340

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We construct equivariant vector bundles over quantum projective spaces using parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of the projective space as a subalgebra in the algebra of functions on the quantum group, we reformulate quantum vector bundles in terms of quantum symmetric pairs. We thus prove the complete reducibility of modules over the corresponding coideal stabilizer subalgebras, via the quantum Frobenius reciprocity.
Keywords: quantum group, quantum projective space, vector bundle, symmetric pair. 
@article{TMF_2019_198_2_a8,
     author = {A. I. Mudrov},
     title = {Equivariant vector bundles over quantum projective spaces},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {326--340},
     publisher = {mathdoc},
     volume = {198},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_2_a8/}
}
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A. I. Mudrov. Equivariant vector bundles over quantum projective spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 2, pp. 326-340. http://geodesic.mathdoc.fr/item/TMF_2019_198_2_a8/