A Borel–Weil Theorem for the Irreducible Quantum Flag Manifolds

Abstract We establish a noncommutative generalisation of the Borel–Weil theorem for Heckenberger–Kolb calculi irreducible quantum flag manifolds ${\mathcal {O}}_q(G/L_S)$, generalising previous work Grassmannians {O}}_q(\textrm {Gr}_{n,m})$. As direct consequence we get novel differential geometric presentation coordinate rings $S_q[G/L_S]$ manifolds. The proof is formulated in terms principal bundles, and recently introduced notion pair, uses Heckenberger Kolb first-order calculus Possion homogeneous spaces {O}}_q(G/L^{\,\textrm {s}}_S)$.