Note on reducibility of parabolic induction for hermitian quaternionic groups over $p$-adic fields

Abstract

In this paper we study the reducibility of certain class of parabolically induced representations of $p$-adic hermitian quaternionic groups. We use the Jacquet modules techniques and the theory of $R$-groups to extend the reducibility results of Tadi\'{c} for split classical groups to the case of arbitrary hermitian quaternionic group.