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On reducibility and unitarizability for classical \(p\)-adic groups, some general results. (English) Zbl 1162.22016
The goal of this paper is to demonstrate the following results about the parabolic induction of classical \(p\)-adic groups: (i) a sufficient condition that the parabolically induced representation is irreducible if its parts, \(\pi\) and \(\sigma\), are irreducible; (ii) some upper bounds related to weakly real irreducible unitarizable representations; and (iii) the identification of some irreducible sub-quotients parabolically induced representations.

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
22E35 Analysis on \(p\)-adic Lie groups
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