The structure of Humphreys-Verma modules for projective spaces
type: Item
instance of: scholarly article
title: The structure of Humphreys-Verma modules for projective spaces
zbMATH Open document ID: 1194.17011
author: Masaharu Kaneda
published in: Journal of Algebra
publication date: 2009-09-10T00:00:00Z
review text: Let \(E\) be a finite dimensional linear space over an algebraically closed field \(\mathbf k\) of positive characteristic, \(G=\text{GL}(E)\), and \(P\) a parabolic subgroup of \(G\) such that \(G/P\) is a projective space over \(\mathbf k\). Let \(G_1\) be the Frobenius kernel of \(G\) and \(T\) a maximal torus of \(P\). The author determined the \(G_1T\)-structure on all \(G_1P\)-modules induced from \(1\)-dimensional \(P\)-modules. They are all multiplicity-free and uniserial.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 5602650
zbMATH Keywords: Induced modules
zbMATH Keywords: Positive characteristic
zbMATH Keywords: projective space
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.04.009
OpenAlex ID: W2028441908
cites work: Loewy Series of Modules for the First Frobenius Kernel in a Reductive Algebraic Group
cites work: Über Differentialoperatoren und \({\mathcal D}\)-Moduln in positiver Charakteristik. (On differential operators and \({\mathcal D}\)- modules in positive characteristic)
cites work: Q3416324
cites work: Q3752572
DOI: 10.1016/J.JALGEBRA.2009.04.009
description: scientific article; zbMATH DE number 5602650