Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 2, pp. 301311 (2010) 

Berezin quantization for discrete seriesBenjamin CahenUniversité de Metz, UFRMIM, Département de mathématiques, LMMAS, ISGMPBât. A, Ile du Saulcy 57045, Metz cedex 01, France, email: cahen@univmetz.frAbstract: Let $M=G/K$ be a Hermitian symmetric space of the noncompact type and $\pi$ be a discrete series representation of $G$ which is holomorphically induced from a unitary character of $K$. We give explicit formulas for the Berezin symbols of the operators $\pi (g)$ ($g\in G$) and $d\pi (X)$ ($X$ in the Lie algebra of $G$). We show that the Berezin quantization on $G/K$ provides an adapted symbol calculus in the sense of [C]. [C] Cahen, B.: Weyl quantization for semidirect products. Differ. Geom. Appl. {\bf 25} (2007), 177190. Keywords: Berezin quantization, Berezin symbol, Hermitian symmetric space of the noncompact type, semisimple noncompact Lie group, irreducible unitary representation, discrete series representation, coherent states, adapted symbol calculus, adjoint orbit Classification (MSC2000): 22E46, 32M10, 32M15, 81S10 Full text of the article (for subscribers):
Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.
© 2010 Heldermann Verlag
