Branes and quantization

The problem of quantizing a symplectic manifold (M, omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M, omega) is the space of (B(cc), B') strings, where B(cc) and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and B(cc) is a space-filling coisotropic A-brane. B' is supported on M, and the choice of omega is encoded in the choice of B(cc). As an example, we describe from this point of view the representations of the group SL(2, R). Another application is to Chern-Simons gauge theory.