Splitting criteria for vector bundles on minuscule homogeneous varieties

TL;DR

This paper establishes a criterion for when vector bundles on minuscule homogeneous varieties split into line bundles, based on their behavior on certain subvarieties, with a detailed case analysis.

Contribution

It provides a new splitting criterion for vector bundles on minuscule homogeneous varieties, linking global splitting to restrictions on specific subvarieties.

Findings

Vector bundles split if and only if their restrictions to unions of 2D Schubert subvarieties split.

A case-by-case analysis confirms the criterion.

The result simplifies understanding of vector bundle splitting on these varieties.

Abstract

I prove that a vector bundle on a minuscule homogeneous variety splits into a direct sum of line bundles if and only if its restriction to the union of two-dimensional Schubert subvarieties splits. A case-by-case analysis is done.