Equivariant vector bundles over quantum projective spaces

TL;DR

This paper constructs and analyzes equivariant vector bundles over quantum projective spaces using quantum group representations, establishing their reducibility and reformulating their structure through quantum symmetric pairs.

Contribution

It introduces a new approach to quantum vector bundles via parabolic Verma modules and quantum symmetric pairs, proving their complete reducibility.

Findings

Complete reducibility of modules over coideal stabilizer subalgebras

Reformulation of quantum vector bundles using quantum symmetric pairs

Construction of equivariant vector bundles over quantum projective spaces

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.