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Tensor Product Realizations of Simple Torsion Free Modules
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2001
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