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The Torsion Free Pieri Formula

Published online by Cambridge University Press:  20 November 2018

D. J. Britten  and
F. W. Lemire
D. J. Britten
Affiliation:
Department of Mathematics University of Windsor Windsor, Ontario N9B 3P4
F. W. Lemire
Affiliation:
Department of Mathematics University of Windsor Windsor, Ontario N9B 3P4
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Abstract

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Central to the study of simple infinite dimensional $g\ell (n,\,\mathbb{C})$-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.

Keywords

17B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 2 , 01 April 1998 , pp. 266 - 289
Copyright
Copyright © Canadian Mathematical Society 1998

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