A constraint on existence of torsion free lie modules.

For any simple Lie algebra L with any maximal toral subalgebra H, the classification of all simple H diagonalizable L modules having a finite dimensional weight space is known to depend on determining the simple torsion free L modules of finite degree. It is further known that the only simple Lie algebras which admit simple torsion free modules of finite degree are those of types A\sb{n-1} and C\sb{m}. For the case of A\sb{n-1} we show that there are no simple torsion free A\sb{n-1} modules of degree k for $n\ge5$ and $2\le k\le n - 3.$ We conclude with some examples showing that there exist simple torsion free A\sb{n-1} modules of degrees 1, $n - 2$ and $n - 1,$ whenever $n\ge3.$Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1992 .T376. Source: Masters Abstracts International, Volume: 31-04, page: 1811. Thesis (M.Sc.)--University of Windsor (Canada), 1992