Window equivalences via categorical sl(2) actions

TL;DR

This paper explores two different methods to establish derived equivalences for stratified Mukai flops of cotangent bundles of Grassmannians, connecting geometric categorical sl(2) actions with matrix factorizations via Knörrer periodicity.

Contribution

It demonstrates the equivalence of two approaches—geometric categorical sl(2) actions and matrix factorizations—using Knörrer periodicity in the context of stratified Mukai flops.

Findings

Established the equivalence of two derived equivalence approaches.

Connected geometric and algebraic methods via Knörrer periodicity.

Enhanced understanding of derived categories in symplectic geometry.

Abstract

We identify two distinct approaches to the derived equivalence for the stratified Mukai flop of cotangent bundles of Grassmannians -- one induced by the geometric categorical sl(2) action, and the other through the magic window category of graded matrix factorizations on the gauged Landau-Ginzburg model -- via the Kn\"orrer periodicity.