Equivariant vector bundles over quantum projective spaces
arXiv:1805.02557 · doi:10.1134/S0040577919020090
Abstract
We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of 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. In this way, we prove complete reducibility of modules over the corresponding coideal stabilizer subalgebras, via the quantum Frobenius reciprocity.
This is a revision of the 2nd part of arXiv:1709.08394, which has been split in two papers. The revised 1st part of arXiv:1709.08394 is kept under the same reference number