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

Naoki Hashimoto; Kenji Taniguchi; Go Yamanaka

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arXiv · 1702.05836

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

Naoki Hashimoto·Kenji Taniguchi·Go Yamanaka

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Abstract

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.

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Naoki Hashimoto, Kenji Taniguchi, Go Yamanaka. 2017-02-20. The socle filtrations of principal series representations of $SL(3,\mathbb{R})$ and $Sp(2,\mathbb{R})$. https://arxiv.org/abs/1702.05836

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