Neveu-Schwarz and operators algebras II: Unitary series and characters

2010/10/01 by Sébastien Palcoux, Palcoux, Sébastien
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.FA #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.1010.0077

30 pages

openalex publication_date 2010/10/01 · arxiv created 2010/10/07 · arxiv updated 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the second of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we give a unitary complete proof of the classification of the unitary series of the Neveu-Schwarz algebra, by the way of GKO construction, Kac determinant and FQS criterion. We then obtain the characters directly, without Feigin-Fuchs resolutions.

Citations

• Operator algebras and conformal field theory
• Subfactors and Connes fusion for twisted loop groups
• Neveu-Schwarz and operators algebras I: Vertex operators superalgebras
• Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion
• Fusion of Positive Energy Representations of LSpin(2n)

Related

• Direct proofs of the Feigin-Fuchs character formula for unitary representations of the Virasoro algebra
• Kac-Moody and Virasoro algebras
• Weyl groups, the Dirac inequality, and isolated unitary unramified representations
• Indecomposable characters of infinite dimensional groups associated with operator algebras
• The Hilbert series of algebras of Veronese type