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We introduce Morse branes in the Fukaya category of a holomorphic symplecticmanifold, with the goal of constructing tilting objects in the category. Wegive a construction of a class of Morse branes in the cotangent bundles, andapply it to give the holomorphic branes that represent the big tilting sheaveson flag varieties.

Representing the big tilting sheaves as holomorphic Morse branes