On the Cohomology of Certain Homogeneous Vector Bundles of G/B in Characteristic Zero

TL;DR

This paper generalizes Demazure's indecomposable modules and computes their cohomology, extending Bott's theorem to a broader class of homogeneous vector bundles in characteristic zero.

Contribution

It introduces a new class of modules generalizing Demazure's and provides their cohomological analysis, expanding understanding of vector bundles on G/B.

Findings

Explicit cohomology calculations for the generalized modules

Extension of Bott's theorem to new modules

Deeper insight into the structure of homogeneous vector bundles

Abstract

In his famous paper [2], Demazure introduced certain indecomposable modules and used them to give a short proof of Bott's theorem. In this paper we consider a generalization of these modules and give their cohomology.