no. 6
Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1755-1818.

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.

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.

DOI: 10.5802/aif.1992
Classification: 17B10,  17B68
Keywords: Neveu-Schwarz and Ramond algebras, Fock modules, Jantzen filtration, Felder-type complex 
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     author = {Iohara, Kenji and Koga, Yoshiyuki},
     title = {Representation theory of {Neveu-Schwarz} and {Ramond} algebras {II:} {Fock} modules},
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     pages = {1755--1818},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {53},
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     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1992/}
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Iohara, Kenji; Koga, Yoshiyuki. Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules. Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1755-1818. doi : 10.5802/aif.1992. https://aif.centre-mersenne.org/articles/10.5802/aif.1992/

[BP] P. Bouwknegt; K. Pilch Fock space resolutions of the Virasoro highest weight modules with c≤1, Lett. Math. Phys., Tome 23 (1991), pp. 193-204 | DOI | MR | Zbl

[FeFu] B. L. Feigin; D. B. Fuchs Representations of the Virasoro algebra (Adv. Stud. Contemp. Math) Tome 7 (1990), pp. 465-554 | Zbl

[Fel] G. Felder BRST approach to minimal models, Nucl. Phys. B, Tome 317 (1989), pp. 215-236 | DOI | MR

[Fel] G. Felder Erratum: "BRST approach to minimal models", Nuclear Phys. B, Tome 324 (1989), pp. 548 | MR

[IK1] K. Iohara; Y. Koga Résolutions de type Bechi-Rouet-Stora-Tyutin pour les super-algèbres de Virasoro N=1, C. R. Acad. Sci. Paris, Sér I, Tome 330 (2000), pp. 541-544 | MR | Zbl

[IK2] K. Iohara; Y. Koga Representation Theory of Neveu-Schwarz and Ramond Algebras I: Verma Modules, Adv. Math, Tome 178 (2003), pp. 1-65 | DOI | MR | Zbl

[Ja] J. C. Jantzen Moduln mit einem höchsten Gewicht, Lect. Notes in Math, Tome 750, Springer-Verlag, 1979 | MR | Zbl

[Sel] A. Selberg Bemerkninger om et multiplet integral, Norsk. Math. Tids. B, Tome 26 (1944), pp. 71-78 | MR | Zbl

[TK] A. Tsuchiya; Y. Kanie Fock Space Representations of the Virasoro Algebra -- Intertwining Operators --, Publ. RIMS Kyoto Univ, Tome 22 (1986), pp. 259-327 | DOI | MR | Zbl

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