Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules
[Théorie des représentations des algèbres de Neveu-Schwarz et de Ramond II : modules de Fock]
Iohara, Kenji1 ; Koga, Yoshiyuki2
1 Kobe University, Faculty of Science, Department of Mathematics, Kobe 657-8501 (Japon)
2 University of Fukui, Faculty of Engineering, Department of Applied Physics, Fukui 910-8507 (Japon)
Annales de l'Institut Fourier, Tome 53 (2003) no. 6, pp. 1755-1818.

En généralisant la filtration de Jantzen, à partir des idées de B. Feigin et D. Fuchs dans “Representations of the Virasoro algebra" paru aux Adv. Stud. Contemp. Math., nous déterminons complètement la structure des modules de Fock pour les super-algèbres de Virasoro N=1. Comme application, nous démontrons l’existence de complexes d’un type de Felder pour les modèles super-minimaux N=1 et leurs descendants. Cet article est une version détaillée de l’article de “Résolution de type Bechi–Rouet–Stora–Tyutin pour les super-algèbres de Virasoro" paru aux CRAS en 2000.

In this article, we study the structure of Fock modules over N=1 super Virasoro algebras. As an application, we construct Bechi-Rouet–Stora–Tyutin type resolutions for N=1 super minimal models and their descendants.

DOI : 10.5802/aif.1992
Classification : 17B10, 17B68
Keywords: Neveu-Schwarz and Ramond algebras, Fock modules, Jantzen filtration, Felder-type complex
Mot clés : algèbres de Neveu-Schwarz et de Ramond, modules de Fock, filtration de Jantzen, complexe d'un type de Felder
Iohara, Kenji 1 ; Koga, Yoshiyuki 2

1 Kobe University, Faculty of Science, Department of Mathematics, Kobe 657-8501 (Japon)
2 University of Fukui, Faculty of Engineering, Department of Applied Physics, Fukui 910-8507 (Japon) 
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     title = {Representation theory of {Neveu-Schwarz} and {Ramond} algebras {II:} {Fock} modules},
     journal = {Annales de l'Institut Fourier},
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Iohara, Kenji; Koga, Yoshiyuki. Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules. Annales de l'Institut Fourier, Tome 53 (2003) no. 6, pp. 1755-1818. doi : 10.5802/aif.1992. https://www.numdam.org/articles/10.5802/aif.1992/

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