Translation and cancellation of socle series patterns
type: Item
instance of: scholarly article
title: Translation and cancellation of socle series patterns
zbMATH Open document ID: 0668.20034
author: Yuanhuai Bai
author: Kexin Wen
author: Jianpan Wang
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Let G be a semi simple algebraic group over a field of prime characteristic and let \(G_ n\) denote the nth Frobenius kernel in G. Also let B be a Borel subgroup. The authors study the relations between induction from B to \(G_ nB\) and induction from B to G. Their main theorem says that for certain 1-dimensional B-modules \(\lambda\), the socle series of \(Ind^ G_ B\lambda\) may be obtained by applying \(Ind^ G_{G_ nB}\) to the \(G_ n\)-socle series of \(Ind_{G_ n}^{G_ nB}\lambda\). This is a generalization of a theorem by the reviewer [see Math. Z. 194, 127-142 (1987; Zbl 0595.20038)].
reviewed by: Henning Haahr Andersen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4093755
zbMATH Keywords: induced modules
zbMATH Keywords: Weyl modules
zbMATH Keywords: multiplicities
zbMATH Keywords: semi simple algebraic group
zbMATH Keywords: Frobenius kernel
zbMATH Keywords: Borel subgroup
zbMATH Keywords: induction
zbMATH Keywords: socle series
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227927
OpenAlex ID: W2061424985
cites work: The first cohomology group of a line bundle on G/B
cites work: The strong linkage principle.
cites work: Jantzen's filtrations of Weyl modules
cites work: On the Generic Structure of Cohomology Modules for Semisimple Algebraic Groups
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: Q3800267
cites work: Q4064209
DOI: 10.2748/TMJ/1178227927
description: scientific article; zbMATH DE number 4093755