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

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.

💡 Research Summary

The paper develops a systematic method for constructing derived equivalences between algebraic varieties by exploiting strong categorical sl(2) actions, following the framework introduced by Chuang and Rouquier. The authors first recall the notion of a strong categorical sl(2) action on a triangulated category: it consists of two exact endofunctors E and F, together with natural transformations that satisfy the sl(2) relations at the categorical level, and a collection of tilting objects that generate each weight subcategory. The “strong” condition means that for each weight λ the subcategory is generated by a tilting object T_λ, and that the functors E and F shift weights by ±2 while preserving the tilting structure.

With this structure in place, the authors define the key “translation functor”
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