Tensor Product Realizations of Simple Torsion Free Modules

http://dx.doi.org/10.4153/CJM-2001-010-x
Canad. J. Math. 53(2001), 225-243

  Published:2001-04-01
 Printed: Apr 2001

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.