A positive characteristic resolution problem for \(\text{SL}(3,k)\)
type: Item
instance of: scholarly article
title: A positive characteristic resolution problem for \(\text{SL}(3,k)\)
zbMATH Open document ID: 0899.20021
author: Mary Lynn Reed
published in: Journal of Algebra
publication date: 1998-07-01T00:00:00Z
review text: This article concerns the theory of rational representations of \(\text{SL}(3,k)\) in case \(\text{char }k=p>0\). For a given regular weight in the fundamental box the author constructs a complex of standard \(G_1B\)-modules with the property, that its highest non-vanishing homology is the irreducible representation with this highest weight and the characters of the other homology groups are known. The complexes remind of BGG-resolutions but they are not exact.
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1106633
zbMATH Keywords: BGG-resolutions
zbMATH Keywords: restricted representations
zbMATH Keywords: semisimple algebraic groups
zbMATH Keywords: rational representations
zbMATH Keywords: irreducible representations
zbMATH Keywords: highest weights
reviewed by: Wolfgang Soergel
MaRDI profile type: Publication
full work available at URL: jabr.1997.7102
OpenAlex ID: W1975109140
cites work: Q4107261
cites work: The submodule structure of Weyl modules for \(SL_ 3\)
cites work: The structure of certain highest weight modules for \(SL_ 3\)
cites work: Q3797389
cites work: A geometric approach to the structure of sl(2,k) weyl modules
DOI: 10.1006/JABR.1997.7102
description: scientific article; zbMATH DE number 1106633