A remark on Berezin's quantization and cut locus

Abstract

The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and two-point functions are defined when one variable does not belong to the cut locus of the other one.Comment: 8 pages, Latex2e, ams fonts, to appear in "Quantizations, Deformations and Coherent States", Edited by S. Twareque Ali, A. Odzijewicz and A. Strasburger, Proceedings of the XV Workshop on Geometric Methods in Physics, Bia\l owie\.{z}a, Poland, 1-7 july 1996, Rep. Math. Phys