Structure of cohomology modules of linear bundles over \(G/B\)
type: Item
instance of: scholarly article
title: Structure of cohomology modules of linear bundles over \(G/B\)
zbMATH Open document ID: 0941.14019
DOI: 10.1007/BF02356059
author: A. M. Adamovich
published in: Mathematical Notes
publication date: 1999-04-27T00:00:00Z
review text: Let \(G\) be a connected, simply connected semi-simple algebraic group over an algebraically closed field of positive characteristic, and let \(B \subset G\) be a Borel subgroup. The author studies the representation of \(G\) on the cohomology of line bundles over the homogenenous space \(G/B\) defined by certain characters of \(B\). He obtains submodules and quotient modules of these \(G\)-modules. The results generalize work of \textit{J. E. Humphreys} [Commun. Algebra 12, 2665-2677 (1984; Zbl 0546.20036)] on the structure of Weyl modules.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14F25
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 1256788
zbMATH Keywords: semisimple algebraic groups
zbMATH Keywords: Weyl modules
zbMATH Keywords: flag spaces
zbMATH Keywords: cohomology of line bundles
zbMATH Keywords: homogeneous space
reviewed by: Jürgen Hausen
MaRDI profile type: Publication
cites work: On the structure of Weyl modules
cites work: On the Generic Structure of Cohomology Modules for Semisimple Algebraic Groups
cites work: The strong linkage principle.
full work available at URL: https://doi.org/10.1007/bf02356059
OpenAlex ID: W1982810414
description: scientific article; zbMATH DE number 1256788