Quantization and Isotropic Submanifolds

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