A Generalized Bott-Borel-Weil Theorem

Abstract

The Borel-Weil Theorem gives a geometric realization of each irreducible representation of a compact connected semisimple Lie group G. Equivalently, this is a realization of each irreducible holomorphic representation of the complexification G_ℂ of G. The realization is in the space of holomorphic sections of a holomorphic line bundle over the flag variety of G.