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

Neven Grbac; Nevena Jurčević Peček

Vol. 23 No. 2 (2018)

Regular Articles

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

Published 2017-11-02

Neven Grbac
Nevena Jurčević Peček

Neven Grbac
Department of Mathematics, University of Rijeka

Nevena Jurčević Peček
Department of Mathematics, University of Rijeka

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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.

Keywords

Hermitian quaternionic groups, parabolically induced representations, reducibility, Jacquet modules, structural formula, R-groups

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