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We construct an equivalence of categories from a strong categorical  sl (2) action, following the work of Chuang–Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.

Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩 2 actions