Irreducible graded \(A_ 1^{(1)}\)-modules
type: Item
instance of: scholarly article
title: Irreducible graded \(A_ 1^{(1)}\)-modules
zbMATH Open document ID: 0822.17026
DOI: 10.1007/BF01077066
publication date: 1994-05-18T00:00:00Z
review text: Consider the algebra \({\mathfrak g} = sl(2, \mathbb{C})\) with a standard basis \(e,f,h\), the current algebra \(\widehat {\mathfrak g} = {\mathfrak g} \otimes \mathbb{C} [t,t^{-1}]\), and its one-dimensional central extension \(\widetilde {\mathfrak g} = \widetilde {\mathfrak g} \oplus \mathbb{C} z\). We introduce the \(\mathbb{Z}^ 2\)-gradation in \(\widehat {\mathfrak g}\) by \(\deg e = (1,0)\), \(\deg f = (-1,0)\), \(\deg h = \deg z = (0,0)\), \(\deg x \otimes t^ n = \deg x + (n,n)\); let \(K\) be the category of \(\mathbb{Z}^ 2\)-graded \(\widetilde {\mathfrak g}\)-modules. In particular, \(K\) contains Verma modules, generalized Verma modules, and their irreducible factor modules. In this note we construct new series of irreducible \(\mathbb{Z}^ 2\)-graded \(\widetilde {\mathfrak g}\)-modules and analogues of Verma modules as well.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 560999
zbMATH Keywords: irreducible graded modules
zbMATH Keywords: generalized Verma modules
author: Vyacheslav Futorny
MaRDI profile type: Publication
cites work: Remarks on the perturbation theory for problems of Mathieu type
cites work: Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
cites work: Resonance regions for Mathieu type dynamical systems on a torus
cites work: Resonance regions for families of torus maps
full work available at URL: https://doi.org/10.1007/bf01077066
OpenAlex ID: W1976765258
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 560999