Extensions of the Jacobi identity for relative untwisted vertex operators, and generating function identities for untwisted standard modules: The \(A^{(1)}_ 1\)-case
type: Item
instance of: scholarly article
title: Extensions of the Jacobi identity for relative untwisted vertex operators, and generating function identities for untwisted standard modules: The \(A^{(1)}_ 1\)-case
zbMATH Open document ID: 0837.17013
DOI: 10.1016/0022-4049(94)00037-J
author: Cristiano Husu
published in: Journal of Pure and Applied Algebra
publication date: 1995-04-10T00:00:00Z
review text: The Jacobi identity for two relative untwisted vertex operators was given by \textit{C. Dong} and \textit{J. Lepowsky} [Proc. XIIth Int. Colloq. on Group Theoretical Methods in Physics, Ste-Adele 1988, 235-238 (World Scientific, Singapore, 1989)]. The author of this paper extends the Jacobi identity to an analogue for a finite number of relative untwisted vertex operators associated with the \(A_1\)-root lattice. Such an extension can be used to reinterpret certain results in \textit{J. Lepowsky} and \textit{R. L. Wilson}'s work on the standard modules of \(A_1^{(1)}\) [Invent. Math. 79, 417-442 (1985; Zbl 0577.17010)], and \textit{J. Lepowsky} and \textit{M. Primc}'s work [Contemp. Math. 46 (1985; Zbl 0569.17007)].
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 741484
zbMATH Keywords: Jacobi identity
zbMATH Keywords: vertex operators
zbMATH Keywords: standard modules
reviewed by: Xiaoping Xu
MaRDI profile type: Publication
cites work: Generalized vertex algebras and relative vertex operators
cites work: The algebraic structure of relative twisted vertex operators
cites work: Basic representations of affine Lie algebras and dual resonance models
cites work: Q3792881
cites work: Extensions of the Jacobi identity for vertex operators, and standard 𝐴⁽¹⁾₁-modules
cites work: Q3320568
cites work: Q3220720
cites work: Construction of the affine Lie algebra \(A^{(1)}_1\)
cites work: A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
cites work: The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
cites work: The structure of standard modules. II: The case \(A_ 1^{(1)}\), principal gradation
cites work: Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities
cites work: Unitary representations of some infinite dimensional groups
description: scientific article; zbMATH DE number 741484