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

TL;DR

This paper constructs a categorical sl(2) action to establish an explicit equivalence between the derived categories of coherent sheaves on cotangent bundles of complementary Grassmannians, advancing understanding of geometric representation theory.

Contribution

It introduces a new categorical sl(2) action framework to explicitly relate derived categories of cotangent bundles of Grassmannians.

Findings

Established a categorical sl(2) action for Grassmannian cotangent bundles

Constructed an explicit equivalence between derived categories

Extended the work of Chuang-Rouquier to geometric settings

Abstract

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.