On the composition series of the standard Whittaker (𝔤,𝔎)-modules

Taniguchi, Kenji

doi:10.1090/S0002-9947-2012-05801-6

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

Trans. Amer. Math. Soc. 365 (2013), 3899-3922 Request permission

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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