The torsion free Pieri formula
Printed: Apr 1998
D. J. Britten
F. W. Lemire
Central to the study of simple infinite dimensional
$g\ell(n, \Bbb C)$-modules having finite dimensional weight spaces are the
torsion free modules. All degree $1$ torsion free modules are known.
Torsion free modules of arbitrary degree can be constructed by tensoring
torsion free modules of degree $1$ with finite dimensional simple modules.
In this paper, the central characters of such a tensor product module are
shown to be given by a Pieri-like formula, complete reducibility is
established when these central characters are distinct and an example
is presented illustrating the existence of a nonsimple indecomposable
submodule when these characters are not distinct.
17B10 - Representations, algebraic theory (weights)