The socle filtrations of principal series representations of $SL(3,\mathbb{R})$ and $Sp(2,\mathbb{R})$

Naoki Hashimoto, Kenji Taniguchi, Go Yamanaka

Published 2017-02-20Version 1

We study the structure of the $(\mathfrak{g},K)$-modules of the principal series representations of $SL(3,\mathbb{R})$ and $Sp(2,\mathbb{R})$ induced from minimal parabolic subgroups, in the case when the infinitesimal character is nonsingular. The composition factors of these modules are known by Kazhdan-Lusztig-Vogan conjecture. In this paper, we give complete descriptions of the socle filtrations of these modules.