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# Tensor Product Realizations of Simple Torsion Free Modules

Published:2001-04-01
Printed: Apr 2001
• D. J. Britten
• F. W. Lemire
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## Abstract

Let $\calG$ be a finite dimensional simple Lie algebra over the complex numbers $C$. Fernando reduced the classification of infinite dimensional simple $\calG$-modules with a finite dimensional weight space to determining the simple torsion free $\calG$-modules for $\calG$ 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.
 MSC Classifications: 17B10 - Representations, algebraic theory (weights)