Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 175-190 (2007)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Weyl quantization for principal series

Benjamin Cahen

Université de Metz, UFR-MIM, Département de mathématiques
LMMAS, ISGMP-Bât. A, Ile du Saulcy 57045, Metz cedex 01, France

Abstract: Let $G$ be a connected semisimple non-compact Lie group and $\pi$ a principal series representation of $G$. Let $\cal O$ be the coadjoint orbit of $G$ associated by the Kirillov-Kostant method of orbits to the representation $\pi$. By dequantizing $\pi$ we construct an explicit symplectomorphism between a dense open set of $\cal O$ and a symplectic product ${\mathbb R}^{2n}\times{\cal O}'$ where ${\cal O}' $ is a coadjoint orbit of a compact subgroup of $G$. This allows us to obtain a Weyl correspondence on $\cal O$ which is adapted to the representation $\pi$ in the sense of [6].

Keywords: Principal series representations, coadjoint orbits, Weyl quantization, Berezin quantization, dequantization.

Classification (MSC2000): 81S10, 22E46

Full text of the article:

Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

© 2007 Heldermann Verlag
© 2007–2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition