On the derived category of the Cayley plane II

TL;DR

This paper constructs a full strongly exceptional collection of 27 homogeneous vector bundles on the Cayley plane, a rational homogeneous space of E6, advancing the understanding of its derived category structure.

Contribution

It introduces a new full strongly exceptional collection of homogeneous vector bundles on the Cayley plane, related to previous work, and demonstrates its Lefschetz property.

Findings

Established a full strongly exceptional collection of 27 bundles.

The collection is a Lefschetz collection with respect to the minimal embedding.

Connects to prior work by the second author on similar collections.

Abstract

We find a full strongly exceptional collection for the Cayley plane OP2, the simplest rational homogeneous space of the exceptional group E6. This collection, closely related to the one given by the second author in [J. Algebra, 330:177-187, 2011], consists of 27 vector bundles which are homogeneous for the group E6, and is a Lefschetz collection with respect to the minimal equivariant embedding of OP2.