The irreducible characters of the Lie superalgebras of type \(A(n,m)\) and filtrations of their Kac modules
type: Item
instance of: scholarly article
title: The irreducible characters of the Lie superalgebras of type \(A(n,m)\) and filtrations of their Kac modules
zbMATH Open document ID: 0873.17002
DOI: 10.1007/BF02785543
author: Avital Frumkin
published in: Israel Journal of Mathematics
publication date: 1997-05-31T00:00:00Z
review text: The author considers the Lie superalgebra \(G=\text{ sl}(n,m)\) and its Kac modules [\textit{V. G. Kac}, Lect. Notes Math. 676, 597-626 (1978; Zbl 0388.17002)]. These Kac modules are highest weight modules \(K_\lambda\) which are in general indecomposable, unless the highest weight \(\lambda\) is typical, in which case they are simple. The author studies the case when \(\lambda=\phi\), where the highest weight \(\phi\) is trivial with respect to \(\text{ sl}(n)\). An expression for the contravariant form on \(K_\phi\) is given, and the filtration associated to this form is shown to be semisimple. Following this, a recursion formula is obtained for obtaining the contravariant form and the characters of each composition factor in the Kac module \(K_\lambda\) for arbitrary \(\lambda\).
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 997625
zbMATH Keywords: Lie superalgebra \(\text{sl}(n,m)\)
zbMATH Keywords: characters
zbMATH Keywords: Kac module
zbMATH Keywords: highest weight modules
zbMATH Keywords: contravariant form
zbMATH Keywords: filtration
MaRDI profile type: Publication
cites work: Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
cites work: Contra-variant form on Kac's modules and some series compositions
cites work: Q3952291
cites work: Lie superalgebras
cites work: Q4168737
cites work: Q3820760
cites work: Lie algebra cohomology and the generalized Borel-Weil theorem
cites work: A character formula for singly atypical modules of the lie superalgebra sl(m/n)
full work available at URL: https://doi.org/10.1007/bf02785543
OpenAlex ID: W2067536587
description: scientific article; zbMATH DE number 997625