Reducibility of some induced representations of 𝑝-adic unitary groups

Murnaghan, Fiona; Repka, Joe

doi:10.1090/S0002-9947-99-02289-8

Reducibility of some induced representations of $p$-adic unitary groups
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by Fiona Murnaghan and Joe Repka

Trans. Amer. Math. Soc. 351 (1999), 193-210

DOI: https://doi.org/10.1090/S0002-9947-99-02289-8

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Abstract:

In this paper we study reducibility of those representations of quasi-split unitary $p$-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to a simple condition on the admissible character.

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