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 semiclassical properties using the off-diagonal expansion of the Bergman kernel. We then show how these results extend to the case of noncompact orbifolds and give an application to relative Poincaré series in the theory of automorphic forms.