  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 (Bcc,B')
strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian
A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M,
and the choice of \omega is encoded in the choice of Bcc. 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.
