$SO(3)$-Berezin-Toeplitz quantization and the AJ conjecture

Abstract

We investigate the Berezin-Toeplitz operators that operate on the geometric quantized space corresponding to the $SO(3)$-Witten-Chern-Simons theory. We conjecture that the $SO(3)$-Berezin-Toeplitz operators quantized from the A-polynomial annihilate the corresponding $SO(3)$-knot states.