Highest weight modules over certain quasigraded Lie algebras on elliptic curves
type: Item
instance of: scholarly article
title: Highest weight modules over certain quasigraded Lie algebras on elliptic curves
zbMATH Open document ID: 0820.17037
DOI: 10.1007/BF01075634
publication date: 1994-07-06T00:00:00Z
review text: [For definitions and notations see the preceding review (Zbl 0820.17036).] In this paper the author studies certain representations of the higher genus affine Kac-Moody algebras. He introduces the concept of quasi-graded highest weight modules. One important observation is the fact that one should drop the assumption that there is only one highest weight vector. He studies representations which depend on 2 such vectors. It turns our that in the class of quasi-graded highest weight modules these modules can be irreducible. He shows that the modules are the direct sum of subspaces of odd resp. even parity, and that each of them has its own highest weight vector. The action of the algebra on each of these subspaces considered modulo the other subspace defines a highest weight module on it for a certain Kac-Moody algebra of genus 0. In terms of Verma modules, a classification of irreducible modules is given.
reviewed by: M. Schlichenmaier
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 571846
zbMATH Keywords: Krichever-Novikov algebras
zbMATH Keywords: Heisenberg algebras
zbMATH Keywords: higher genus affine Kac-Moody algebras
zbMATH Keywords: quasi-graded highest weight modules
zbMATH Keywords: Verma modules
zbMATH Keywords: irreducible modules
author: O. K. Sheinman
MaRDI profile type: Publication
cites work: Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons
cites work: Representations of the Heisenberg algebra on a Riemann surface
cites work: Q4065692
full work available at URL: https://doi.org/10.1007/bf01075634
OpenAlex ID: W1976312863
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 571846