Abstract
When combined with mirror symmetry, the A-model approach to quantization
leads to a fairly simple and tractable problem.
The most interesting part of the problem then becomes finding the mirror
of the coisotropic brane.
We illustrate how it can be addressed in a number of interesting examples
related to representation theory and gauge theory,
in which mirror geometry is naturally associated with the Langlands dual group.
Hyperholomorphic sheaves and (B,B,B ) branes play an important role
in the B-model approach to quantization.