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On modules of bounded multiplicities for the symplectic algebras

Author(s): D. J. Britten; F. W. Lemire
Journal: Trans. Amer. Math. Soc. 351 (1999), 3413-3431.
MSC (1991): Primary 17B10
Posted: April 20, 1999
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Abstract | References | Similar articles | Additional information

Abstract: Simple infinite dimensional highest weight modules having
bounded weight multipicities are classified as submodules of a tensor product. Also, it is shown that a simple torsion free module of finite degree tensored with a finite dimensional module is completely reducible.

References:

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G.M. Benkart, D.J. Britten, and F.W. Lemire, Modules with Bounded Weight Multiplicities for Simple Lie Algebras, Math. Z. 225 (1997), 333-353. MR 98h:17004

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D.J. Britten, V. Futorny, and F.W. Lemire, Simple $A_2$ modules with a finite dimensional weight space, Comm. in Algebra 23 (1995), 467-510. MR 95k:17005

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D.J. Britten, J. Hooper, and F.W. Lemire, Simple $C_n$-modules with multiplicities 1 and applications, Canad. Jour. of Physics 72 (1994), 326-335. MR 96d:17004

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D.J. Britten and F.W. Lemire, A Pieri-like Formula for Torsion Free Modules, Canad. J. Math. 50 (1998), 266-289.

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O. Mathieu, Classification of Irreducible Weight Modules, preprint

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Additional Information:

D. J. Britten
Affiliation: Department of Mathematics, University of Windsor, Windsor, Ontario, Canada N9B 3P4

F. W. Lemire
Affiliation: Department of Mathematics, University of Windsor, Windsor, Ontario, Canada N9B 3P4

DOI: 10.1090/S0002-9947-99-02338-7
PII: S 0002-9947(99)02338-7
Received by editor(s): April 15, 1997
Posted: April 20, 1999
Additional Notes: The first author was supported in part by NSERC Grant #0GP0008471 and the second author was supported in part by NSERC Grant #0GP0007742
Copyright of article: Copyright 1999, American Mathematical Society

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