Basic representation of the affine superalgebra \(A^{(2)}(0,1)\)
type: Item
instance of: scholarly article
title: Basic representation of the affine superalgebra \(A^{(2)}(0,1)\)
zbMATH Open document ID: 0927.17015
author: George Golitzin
published in: Journal of Algebra
publication date: 1999-12-15T00:00:00Z
review text: In [\textit{G. Golitzin}, J. Algebra 117, No. 1, 198-226 (1988; Zbl 0652.17013)] the author constructed some irreducible highest weight representations of the affine superalgebras \(A^{(4)}(0,2l)\) and \(A^{(2)}(0,2l-1)\). Since his considerations degenerate for \(A^{(2)}(0,1)\), the purpose of the paper under review is to cover also this simplest case. The algebra \(\widetilde{\mathfrak g}(\nu)=A^{(2)}(0,1)\) is the extended twisted loop algebra associated with the finite dimensional simple superalgebra \({\mathfrak g}=A(0,1)=sl(1,2)\) and its Cartan automorphism \(\nu\). The irreducible modules given in the paper are those of fundamental highest weight. They are realized as the tensor product of symmetric and exterior algebras on which \(A^{(2)}(0,1)\) acts by products of vertex operators and operators of Clifford type.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 1271651
zbMATH Keywords: affine Lie superalgebras
zbMATH Keywords: representations of Lie superalgebras
zbMATH Keywords: vertex operators
zbMATH Keywords: highest weight modules
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
full work available at URL: jabr.1996.6536
OpenAlex ID: W1999798834
cites work: Q3739338
cites work: Representation of the affine superalgebras \(A^{(4)}(0,2\ell)\), \(A^{(2)}(0,2\ell -1)\) and their subalgebras \(A_{2\ell}^{(2)}\), \(A^{(2)}_{2\ell -1}\) by vertex operators
cites work: Lie superalgebras
cites work: Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
cites work: Construction of the affine Lie algebra \(A^{(1)}_1\)
cites work: The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
DOI: 10.1006/JABR.1996.6536
description: scientific article; zbMATH DE number 1271651