Essentially typical representations of Lie superalgebras \({\mathfrak gl}(n| m)\) in the Gel'fand-Tsetlin basis
type: Item
instance of: scholarly article
title: Essentially typical representations of Lie superalgebras \({\mathfrak gl}(n| m)\) in the Gel'fand-Tsetlin basis
zbMATH Open document ID: 0707.17017
DOI: 10.1007/BF01078788
author: Elsie Sterbin Gottlieb
publication date: 1989-01-01T00:00:00Z
review text: The paper is devoted to a special class of finite-dimensional irreducible modules with respect to the Lie superalgebra \({\mathfrak gl}(n| m)\). Such a typical module W(n,m) is said to be essentially typical, if there exists no flag of submodules W(n,m)\(\supset...\supset W(n,p)\supset...\supset W(n,1)\) with at least one irreducible \({\mathfrak gl}(n| p)\)-submodule W(n,p). The author modifies the concept of the Gel'fand-Tsetlin basis to the case of essentially typical \({\mathfrak gl}(n| m)\)-module and deduces an explicit formula for the action of \({\mathfrak gl}(n| m)\) in such a basis.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 4160983
zbMATH Keywords: general linear Lie superalgebra
zbMATH Keywords: irreducible modules
zbMATH Keywords: Gel'fand-Tsetlin basis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01078788
OpenAlex ID: W2037321502
published in: Functional Analysis and Its Applications
reviewed by: Ivan Kolář
description: scientific article; zbMATH DE number 4160983