On some representations of twisted affine Lie algebras and combinatorial identities
type: Item
instance of: scholarly article
title: On some representations of twisted affine Lie algebras and combinatorial identities
zbMATH Open document ID: 0774.17029
author: Stefano Capparelli
published in: Journal of Algebra
publication date: 1993-05-16T00:00:00Z
review text: The aim of this paper is to give explicit vertex operator realizations of level two and level three integrable highest weight representations of the affine Lie algebra \(A_ 2^{(2)}\). Using the vertex operator realization of the basic (level one) representation of \(A_ 2^{(2)}\) and the calculus of formal variables the author obtains certain spanning sets for each level two and three representations. Invoking the Rogers- Ramanujan identities it has been shown that the spanning sets for the level two representations are in fact bases for the respective representations. It is conjectured that the spanning sets for the level three representations are also bases.
reviewed by: Kailash C. Misra
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 168585
zbMATH Keywords: vertex operators
zbMATH Keywords: combinatorial identities
zbMATH Keywords: integrable highest weight representations
zbMATH Keywords: affine Lie algebra
zbMATH Keywords: Rogers-Ramanujan identities
Wikidata QID: Q115396328
MaRDI profile type: Publication
full work available at URL: jabr.1993.1017
OpenAlex ID: W2021764109
DOI: 10.1006/JABR.1993.1017
description: scientific article; zbMATH DE number 168585