Canonical tilting bundles: the first nonabelian examples

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.