Modules with highest weight for affine Lie algebras on Riemann surfaces
type: Item
instance of: scholarly article
title: Modules with highest weight for affine Lie algebras on Riemann surfaces
zbMATH Open document ID: 0848.17023
DOI: 10.1007/BF01077040
publication date: 1996-02-25T00:00:00Z
review text: In the global approach to Conformal Field Theory on higher genus Riemann surfaces initiated by Krichever and Novikov one replaces the Virasoro algebra and the related algebras by the corresponding algebras which are given by meromorphic objects with poles only at two points (see the review Zbl 0820.17036 for more background information). Starting from any simple Lie algebra \({\mathfrak g}\) (with associated group \(G)\) the generalized affine Lie algebra \(\widehat {\mathfrak g}\) was introduced by the author [Funct. Anal. Appl. 27, 266-272 (1993; Zbl 0820.17036)]. In the article under review the author defines and studies highest weight representations of these affine type Lie algebras. To study them he introduces the notion of Bloch weights which are analogs of the Bloch spectrum in the theory of completely integrable systems. An analog of the Weyl-Kac character formula is proven.
reviewed by: M. Schlichenmaier
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 30F30
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 846563
zbMATH Keywords: Kac-Moody algebras
zbMATH Keywords: Krichever-Novikov algebras
zbMATH Keywords: affine algebras
zbMATH Keywords: almost graded algebras
zbMATH Keywords: central extensions
zbMATH Keywords: highest weight representations
zbMATH Keywords: Bloch weights
zbMATH Keywords: Weyl-Kac character formula
author: O. K. Sheinman
MaRDI profile type: Publication
cites work: Virasoro-type algebras, Riemann surfaces and strings in Minkowski space
cites work: Representations of the Heisenberg algebra on a Riemann surface
cites work: Orbital theory for affine Lie algebras
cites work: Unitary representations of some infinite dimensional groups
cites work: Structure of representations generated by vectors of highest weight
cites work: Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
cites work: Q4065692
full work available at URL: https://doi.org/10.1007/bf01077040
OpenAlex ID: W2079275286
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 846563