Abstract
Let G be a classical p-adic group. If T is an irreducible tempered representation of such a group and \(\rho \) an irreducible unitary supercuspidal representation of a general linear group, we can form the parabolically induced representation \(\text{ Ind }_P^G (|det|^y \rho \otimes T)\). The main result in this paper is the determination for which \(y \in {\mathbb R}\) the induced representation is reducible. The key technical result in establishing this is the determination of a certain Jacquet module subquotient.
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Research supported in part by NSA Grant H98230-13-1-0237.
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Jantzen, C. Jacquet modules and irrreducibility of induced representations for classical p-adic groups. manuscripta math. 156, 23–55 (2018). https://doi.org/10.1007/s00229-017-0955-2
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DOI: https://doi.org/10.1007/s00229-017-0955-2