Quantization and isotropic submanifolds

Abstract

We introduce the notion of an isotropic quantum state associated with a Bohr-Sommerfeld manifold in the context of Berezin-Toeplitz quantization of general prequantized symplectic manifolds, and we study its semi-classical properties using the off-diagonal expansion of the Bergman kernel. We then show how these results extend to the case of non-compact orbifolds, and give an application to relative Poincaré series in the theory of automorphic forms.

45 pages, final version to appear in Michigan Mathematical Journal