Berezin quantization on generalized flag manifolds

Authors

  • Benjamin Cahen

DOI:

https://doi.org/10.7146/math.scand.a-15106

Abstract

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) (gG) and dπ(X) (Xg). In particular, we recover some results of S. Berceanu and we partially generalize a result of K. H. Neeb.

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Published

2009-09-01

How to Cite

Cahen, B. (2009). Berezin quantization on generalized flag manifolds. MATHEMATICA SCANDINAVICA, 105(1), 66–84. https://doi.org/10.7146/math.scand.a-15106

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Articles