The Torsion Free Pieri Formula

Britten, D. J. ; Lemire, F. W.

Canadian journal of mathematics, Tome 50 (1998) no. 2, pp. 266-289

Résumé

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.

Détail

DOI : 10.4153/CJM-1998-014-8

Mots-clés : 17B10

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