Resumen de Berezin quantization on generalized flag manifolds

Cahen Benjamin

• Let M=G/H be a generalized flag manifold where G is a compact, connected, simply-connected Lie group with Lie algebra g and H is the centralizer of a torus. Let π be a unitary irreducible representation of G which is holomorphically induced from a character of H. Using a complex parametrization of a dense open subset of M, we realize π on a Hilbert space of holomorphic functions. We give explicit expressions for the differential dπ of π and for the Berezin symbols of π(g) (g∈G) and dπ(X) (X∈g). In particular, we recover some results of S. Berceanu and we partially generalize a result of K. H. Neeb.