Highest weight representations of the Lie algebra \(\mathfrak{gl}_{\infty}\)
type: Item
instance of: scholarly article
title: Highest weight representations of the Lie algebra \(\mathfrak{gl}_{\infty}\)
zbMATH Open document ID: 0712.17007
DOI: 10.1007/BF01077927
author: Elsie Sterbin Gottlieb
publication date: 1990-01-01T00:00:00Z
review text: The Lie algebra \(\mathfrak{gl}_{\infty}\) is defined as the set of all infinite matrices \((a_{ij})_{i,j\in\mathbb{Z}}\) with only a finite number of nonzero coefficients. The corresponding group contains all matrices \((A_{ij})_{i,j\in\mathbb{Z}}\), where only a finite number of coefficients \(A_{ik}\) is different from \(\delta_{ij}\). Here irreducible representations of \(\mathfrak{gl}_{\infty}\) are investigated, which are highest weight representations and integrable. The representations are characterized by Gelfand-Tsetlin bases, and explicit forms of the operators are given.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 4171170
zbMATH Keywords: infinite-dimensional Lie algebra
zbMATH Keywords: irreducible representations
zbMATH Keywords: highest weight representations
zbMATH Keywords: Gelfand-Tsetlin bases
Wikidata QID: Q115394301
reviewed by: Günter Czichowski
MaRDI profile type: Publication
cites work: Q3820760
cites work: Spin and wedge representations of infinite-dimensional Lie algebras and groups
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4171170