The University of Southampton
University of Southampton Institutional Repository

Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)

Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)
Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)
In a study of finite-dimensional modules of simple Lie superalgebras, Kac introduced certain indecomposable modules, now known as Kac-modules V-bar(Lambda), which are simple if and only if Lambda is typical. For Lambda atypical, Hughes et al. presented an algorithm to determine all the composition factors of the Kac-module; they conjectured that there exists a bijection between the composition factors of a Kac-module and so-called permissible codes. The aim in this paper is to contribute to the proof of this conjecture. By constructing explicitly the primitive vector, we prove that for any unlinked code there corresponds a composition factor of the Kac-module. It will be proved in another paper that to any linked code there also corresponds a composition factor of the Kac-module. Thus the proof of the Hughes et al. conjecture will be reduced to the problem whether or not each composition factor corresponds to a linked or unlinked code.
0022-2488
5064-5087
Su, Yucai
2a4b746f-abdd-4566-bb6f-7784f8f7daf9
Hughes, J.W.B.
f71a7287-d978-4e9d-abc0-8a72fe6fe636
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Su, Yucai
2a4b746f-abdd-4566-bb6f-7784f8f7daf9
Hughes, J.W.B.
f71a7287-d978-4e9d-abc0-8a72fe6fe636
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706

Su, Yucai, Hughes, J.W.B. and King, R.C. (2000) Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n). Journal of Mathematical Physics, 41 (7), 5064-5087. (doi:10.1063/1.533392).

Record type: Article

Abstract

In a study of finite-dimensional modules of simple Lie superalgebras, Kac introduced certain indecomposable modules, now known as Kac-modules V-bar(Lambda), which are simple if and only if Lambda is typical. For Lambda atypical, Hughes et al. presented an algorithm to determine all the composition factors of the Kac-module; they conjectured that there exists a bijection between the composition factors of a Kac-module and so-called permissible codes. The aim in this paper is to contribute to the proof of this conjecture. By constructing explicitly the primitive vector, we prove that for any unlinked code there corresponds a composition factor of the Kac-module. It will be proved in another paper that to any linked code there also corresponds a composition factor of the Kac-module. Thus the proof of the Hughes et al. conjecture will be reduced to the problem whether or not each composition factor corresponds to a linked or unlinked code.

This record has no associated files available for download.

More information

Published date: 2000

Identifiers

Local EPrints ID: 29521
URI: http://eprints.soton.ac.uk/id/eprint/29521
ISSN: 0022-2488
PURE UUID: 523e3e84-fad2-4223-92e2-907440eb85e1

Catalogue record

Date deposited: 19 Jul 2006
Last modified: 08 Jan 2022 15:53

Export record

Altmetrics

Contributors

Author: Yucai Su
Author: J.W.B. Hughes
Author: R.C. King

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×