Kyoto Journal of Mathematics

Socle filtrations of the standard Whittaker (g,K)-modules of Spin(r,1)

Kenji Taniguchi

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Abstract

Studied are the composition series of the standard Whittaker (g,K)-modules. For a generic infinitesimal character, the structures of these modules are completely understood, but if the infinitesimal character is integral, then there are not so many cases in which the structures of them are known. In this paper, as an example of the integral case, we determine the socle filtrations of the standard Whittaker (g,K)-modules when G is the group Spin(r,1) and the infinitesimal character is regular integral.

Article information

Source
Kyoto J. Math., Volume 55, Number 1 (2015), 43-61.

Dates
First available in Project Euclid: 13 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1426252130

Digital Object Identifier
doi:10.1215/21562261-2848115

Mathematical Reviews number (MathSciNet)
MR3323527

Zentralblatt MATH identifier
1320.22006

Subjects
Primary: 22E46: Semisimple Lie groups and their representations 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}

Keywords
Whittaker module Real reductive group

Citation

Taniguchi, Kenji. Socle filtrations of the standard Whittaker $(\mathfrak{g},K)$ -modules of $\operatorname {Spin}(r,1)$. Kyoto J. Math. 55 (2015), no. 1, 43--61. doi:10.1215/21562261-2848115. https://projecteuclid.org/euclid.kjm/1426252130


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References

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