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Tensor Product Realizations of Simple Torsion Free Modules

Published online by Cambridge University Press:  20 November 2018

D. J. Britten  and
F. W. Lemire
D. J. Britten
Affiliation:
Department of Mathematics University of Windsor Windsor, Ontario N9B 3P4
F. W. Lemire
Affiliation:
Department of Mathematics University of Windsor Windsor, Ontario N9B 3P4
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Abstract

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Let $\mathcal{G}$ be a finite dimensional simple Lie algebra over the complex numbers $C$. Fernando reduced the classification of infinite dimensional simple $\mathcal{G}$-modules with a finite dimensional weight space to determining the simple torsion free $\mathcal{G}$-modules for $\mathcal{G}$ of type $A$ or $C$. These modules were determined by Mathieu and using his work we provide a more elementary construction realizing each one as a submodule of an easily constructed tensor product module.

Keywords

17B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 2 , 01 April 2001 , pp. 225 - 243
Copyright
Copyright © Canadian Mathematical Society 2001

References

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