A BOREL-WEIL THEOREM FOR IRREDUCIBLE QUANTUM FLAG MANIFOLDS

The Borel-Weil theorem is a fundamental result in (classical) geometric representation theory. It realizes each irreducible representation of a complex semisimple Lie algebra as the space of holomorphic sections over a flag manifold. I will give a noncommutative generalization of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the irreducible quantum flag manifolds. Time permitting, I will review the recently introduced notion of principal pairs of quantum homogeneous spaces that allows one to give a proof of the Borel-Weil theorem in the context of quantum principal bundles.