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

Sébastien Palcoux (1)

1 IML - Institut de mathématiques de Luminy

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.

Mots clés: von Neumann algebra; conformal field theory; primary fields; intertwining operator; subfactors; Connes fusion; unitary representations; local algebra; III$_{1}$ factor; bimodules; braiding; supersymmetry; boson; fermion; vertex algebra; Virasoro algebra

Domaines: Algèbres d'opérateurs [math.OA]; Analyse fonctionnelle [math.FA]; Théorie des représentations [math.RT]

Sébastien Palcoux. Neveu-Schwarz and operators algebras II: Unitary series and characters.. 2010. ⟨hal-00522527v2⟩