Realization of coherent state Lie algebras by differential operators

Abstract

A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.

26 pages, AMSART, AMS fonts, to appear in the Proceedings of the International Conference ``Operator Algebras and Mathematical Physics'', June 26 - July 04, 2003, Sinaia, Romania

References in corpus (4)

• Deformation quantization of Poisson manifolds, I
• Differential operators on orbits of coherent states
• The coherent states: old geometrical methods in new quantum clothes
• Linear Hamiltonians on homogeneous Kähler manifolds of coherent states

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• Remarks on the geometry of the extended Siegel--Jacobi upper half-plane
• Wei-Norman and Berezin's equations of motion on the Siegel-Jacobi disk