Sections of homogeneous bundles

TL;DR

This paper presents a method to compute sections of homogeneous vector bundles on rational homogeneous varieties of type ADE using quiver representations, generalizing previous work by Ottaviani and Rubei.

Contribution

The paper introduces a new approach leveraging quiver representations to compute sections of homogeneous bundles on G/P, extending prior results to all ADE types.

Findings

Provides a general method for all ADE types

Establishes an equivalence between bundles and quiver representations

Generalizes previous specific cases

Abstract

In this work we give a method for computing sections of homogeneous vector bundles on any rational homogeneous variety G/P of type ADE. Our main tool is the equivalence of categories between homogeneous vector bundles on G/P and finite dimensional representations of a given quiver with relations. Our result generalizes the work of Ottaviani and Rubei [OR06].