For holomorphic symplectic manifolds admitting SYZ fibrations, the endomorphism algebra of a canonical coisotropic A-brane is isomorphic via SYZ transform to the endomorphism algebra of its mirror B-brane, with the action on Lagrangian branes matching Gukov-Witten quantization on both sides.
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Brane quantization and SYZ mirror symmetry
For holomorphic symplectic manifolds admitting SYZ fibrations, the endomorphism algebra of a canonical coisotropic A-brane is isomorphic via SYZ transform to the endomorphism algebra of its mirror B-brane, with the action on Lagrangian branes matching Gukov-Witten quantization on both sides.