Splitting conjectures for uniform flag bundles

TL;DR

This paper explores conjectures about the diagonalizability of uniform principal bundles on rational homogeneous spaces, extending classical results on uniform vector bundles on projective spaces, and investigates their validity for classical groups.

Contribution

It introduces new conjectures on the diagonalizability of uniform principal bundles and analyzes their validity in the context of classical groups.

Findings

Conjectures extend classical theorems to principal bundles.

Validation of conjectures for classical groups.

Provides insights into the structure of uniform principal bundles.

Abstract

We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the validity of these conjectures in the case of classical groups.