Publication at Faculty of Mathematics and Physics |
2022
Abstract
We establish a noncommutative generalisation of the Borel–Weil theorem for the Heckenberger–Kolb calculi of the irreducible quantum flag manifolds Oq(G/LS), generalising previous work for the quantum Grassmannians Oq(Grn,m). As a direct consequence we get a novel noncommutative differential geometric presentation of the quantum coordinate rings Sq[G/LS] of the irreducible quantum flag manifolds.
The proof is formulated in terms of quantum principal bundles, and the recently introduced notion of a principal pair, and uses the Heckenberger and Kolb first-order differential calculus for the quantum Possion homogeneous spaces Oq(G/LsS)