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Proceedings of the American Mathematical Society

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A module induced from a Whittaker module


Author: Edward McDowell
Journal: Proc. Amer. Math. Soc. 118 (1993), 349-354
MSC: Primary 17B35
DOI: https://doi.org/10.1090/S0002-9939-1993-1143020-0
MathSciNet review: 1143020
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Abstract: In an earlier paper [On modules induced from Whittaker modules, J. Algebra 96 (1985)] we constructed a class of induced modules, over a finite-dimensional semisimple Lie algebra, which includes the Verma modules of Verma [Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968)] and the irreducible Whittaker modules of Kostant [On Whittaker vectors and representation theory, Invent. Math. 48 (1978)]. We proved that every module in this class has finite length and is irreducible most of the time. In this article we present a concrete example of this construction, over $ \operatorname{sl} (3,C)$, showing that proper submodules can exist when the induced module is not a Verma module.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1143020-0
Article copyright: © Copyright 1993 American Mathematical Society