Representation theory of Neveu-Schwarz and Ramond algebras. I: Verma modules.
type: Item
instance of: scholarly article
title: Representation theory of Neveu-Schwarz and Ramond algebras. I: Verma modules.
zbMATH Open document ID: 1048.17005
DOI: 10.1016/S0001-8708(02)00059-2
author: Yoshiyuki Koga
author: Kenji Iohara
published in: Advances in Mathematics
publication date: 2003-08-25T00:00:00Z
review text: 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.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 1970565
zbMATH Keywords: Neveu-Schwarz algebra
zbMATH Keywords: Ramond algebra
zbMATH Keywords: Verma module
zbMATH Keywords: Jantzen filtration
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970565