Highest weight representations of the Neveu-Schwarz and Ramond algebras
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.
scientific article; zbMATH DE number 3968839
scientific article