Representation theory of Neveu-Schwarz and Ramond algebras. I: Verma modules.
The Neveu-Schwarz and Ramond algebras appear as special sectors of the \(N=1\) super Virasoro algebra. In the present paper the authors study the structure of Verma modules for the \(N=1\) super Virasoro algebras, and construct a BGG-type resolution of the irreducible highest weight modules. The paper is a detailed and explanatory version of [\textit{K. Iohara} and \textit{Y. Koga}, C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 5, 381--384 (1999; Zbl 0969.17016)]. Additionally, the authors study morphisms between Verma modules over Neveu-Schwarz and Ramond algebras. It is shown that all non-trivial morphisms between Verma modules over Neveu-Schwarz algebras are injective, whereas there are non-trivial and non-injective morphisms between Verma modules over Ramond algebras. All latter morphisms are completely desribed.
scientific article; zbMATH DE number 1970565