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The torsion free Pieri formula

Published:1998-04-01
Printed: Apr 1998
• D. J. Britten
• F. W. Lemire
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Abstract

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.
 MSC Classifications: 17B10 - Representations, algebraic theory (weights)

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