Very strong linkage for cohomology groups of line bundles on G/B
type: Item
instance of: scholarly article
title: Very strong linkage for cohomology groups of line bundles on G/B
zbMATH Open document ID: 0645.20023
DOI: 10.1016/0021-8693(88)90183-4
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author generalizes the strong linkage principle [the reviewer, J. Reine Angew. Math. 315, 53-59 (1980; Zbl 0439.20026)] for cohomology modules of line bundles on G/B. Here G is a reductive algebraic group over a field of positive characteristic and B is a Borel subgroup. The generalization gives for two p-singular weights \(\lambda\) and \(\mu\) a stronger necessary condition for the simple G-module with highest weight \(\lambda\) to occur as a composition factor in the cohomology of the line bundle on G/B induced by \(\lambda\). The paper also contains an infinitesimal version of the same principle. Recently, \textit{S. Doty} [in a preprint from Loyola Univ. Chicago (1987) entitled, The Strong Linkage Principle] has obtained similar results by starting out with the infinitesimal case and then deducing the principle for G.
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 4051886
zbMATH Keywords: strong linkage principle
zbMATH Keywords: cohomology modules of line bundles
zbMATH Keywords: reductive algebraic group
zbMATH Keywords: Borel subgroup
zbMATH Keywords: p-singular weights
zbMATH Keywords: composition factor
author: Warren J. Wong
reviewed by: Henning Haahr Andersen
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90183-4
OpenAlex ID: W2031892634
cites work: The first cohomology group of a line bundle on G/B
cites work: The strong linkage principle.
cites work: Filtrations of cohomology modules for Chevalley groups
cites work: Q5580319
cites work: Q4128999
cites work: On the structure of the higher cohomology modules of line bundles on G/B
cites work: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
cites work: Homomorphisms between neighbouring Weyl modules
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description: scientific article; zbMATH DE number 4051886