Kyoto Journal of Mathematics

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

Kenji Taniguchi

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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.

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

First available in Project Euclid: 13 March 2015

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Zentralblatt MATH identifier

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}

Whittaker module Real reductive group


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.

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