Canonical tilting bundles: the first nonabelian examples

TL;DR

This paper constructs explicit tilting bundles on cotangent bundles of Grassmannians of 2-planes, linking geometric categorical actions to canonical bases and providing new nonabelian examples in algebraic geometry.

Contribution

It introduces a novel explicit construction of tilting bundles on cotangent bundles of Grassmannians of 2-planes, extending the class of known nonabelian examples.

Findings

Constructed tilting bundles invariant under derived equivalences

Connected tilting bundles to categorical sl(2) actions

Provided a categorical lift of the K-theoretic canonical basis

Abstract

We present an explicit construction of tilting bundles on cotangent bundles of Grassmannians of 2-planes. This construction is based on Kapranov's exceptional collection for the underlying Grassmannians, and utilizes specific iterative extensions. The resulting tilting bundle exhibits invariance under the derived equivalence for the stratified Mukai flop through the geometric categorical sl(2) action, providing a categorical lift of the K-theoretic canonical basis up to shifts.