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We study the structure of the (g, K) -modules of the principal series representations of SL (3, R) and Sp (2, 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.
Hashimoto et al. (Sat,) studied this question.
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