Highest weight representations of the Neveu-Schwarz and Ramond algebras
type: Item
instance of: scholarly article
title: Highest weight representations of the Neveu-Schwarz and Ramond algebras
zbMATH Open document ID: 0601.17001
DOI: 10.1007/BF01209395
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The Virasoro algebra (infinite Witt algebra) has two super-extensions which, after universal central extension, are called the Neveu-Schwarz and the Ramond algebras. These infinite-dimensional Lie superalgebras play an important role in contemporary quantum field theory (superstrings). The authors prove the conjectured formulae for the determinant of the Shapovalov form. An essential intermediate step is the construction of a family of representations which generalize the Fock representations of the Virasoro algebra. The determinant formulae are applied to prove that the highest weight of a Verma module and that of an irreducible subquotient are ''linked''. In an appendix, the authors extend some definitions and classical results about central extensions of Lie algebras to the super-case.
reviewed by: M. Scheunert
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 3968839
zbMATH Keywords: Neveu-Schwarz superalgebra
zbMATH Keywords: Ramond superalgebra
zbMATH Keywords: Shapovalov determinant
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: super-extensions
zbMATH Keywords: highest weight
zbMATH Keywords: Verma module
author: Arne Meurman
author: Alvany Rocha-Caridi
MaRDI profile type: Publication
cites work: Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
cites work: Interpolation of quasilinear operators and inequalities for entire functions in symmetric spaces
cites work: Classical affine algebras
cites work: Spinor representations of affine Lie algebras
cites work: Basic representations of affine Lie algebras and dual resonance models
cites work: A loop of SU(2) gauge fields stable under the Yang-Mills flow
cites work: Q5185738
cites work: Lie algebra homology and the Macdonald-Kac formulas
cites work: Projective unitary positive-energy representations of \(Diff(S^ 1)\)
cites work: Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
cites work: Lie superalgebras
cites work: Spin and wedge representations of infinite-dimensional Lie algebras and groups
cites work: On the structure of Hopf algebras
cites work: Highest Weight Modules Over Graded Lie Algebras: Resolutions, Filtrations and Character Formulas
cites work: Characters of irreducible representations of the Lie algebra of vector fields on the circle
cites work: Unitary representations of some infinite dimensional groups
cites work: On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
description: scientific article; zbMATH DE number 3968839