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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the composition series of the standard Whittaker $ (\mathfrak{g},K)$-modules


Author: Kenji Taniguchi
Journal: Trans. Amer. Math. Soc. 365 (2013), 3899-3922
MSC (2010): Primary 22E46, 22E45
Published electronically: November 6, 2012
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Abstract: For a real reductive linear Lie group $ G$, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker $ (\mathfrak{g},K)$-modules, which are $ K$-admissible submodules of the space of Whittaker functions. We first determine the structures of them when the infinitesimal characters characterizing them are generic. As an example of the integral case, we determine the composition series of the standard Whittaker $ (\mathfrak{g},K)$-module when $ G$ is the group $ U(n,1)$ and the infinitesimal character is regular integral.


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Additional Information

Kenji Taniguchi
Affiliation: Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1, Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
Email: taniken@gem.aoyama.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05801-6
PII: S 0002-9947(2012)05801-6
Keywords: Whittaker modules
Received by editor(s): February 24, 2011
Received by editor(s) in revised form: January 26, 2012
Published electronically: November 6, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.