Abstract
It was recently shown (by the second author and Di ' az Garci ' a, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold (9q(G/LS) admits a unique (9q(G)-covariant connection with respect to the Heckenberger- Kolb differential calculus ohm 1q(G/LS). In this paper we show that these connections are bimodule connections with an invertible associated bimodule map.
This is proved by applying general results of Beggs and Majid, on principal connections for quantum principal bundles, to the quantum principal bundle presentation of the Heckenberger-Kolb calculi recently constructed by the authors and Di ' az Garci ' a. Explicit presentations of the associated bimodule maps are given first in terms of generalised quantum determinants, then in terms of the FRT presentation of the algebra (9q(G), and finally in terms of Takeuchi's categorical equivalence for relative Hopf modules.