On reducibility of parabolic induction

Jacquet modules of 𝑝-adic general linear groups

“…[Tad1], [Tad2], [Tad3]) on the use of Jacquet modules in analyzing induced representations. Section 3.1 of this paper contains such an analysis, though most of this paper is focused on the calculation of the Jacquet modules themselves.…”

Reducibility of some generalized principal series of the metaplectic group

“…The second lemma is the metaplectic version of a case of Lemma 3.8 of [19] and the same proof works here, changing only group notation. (Ind…”

“…In the proof of the main theorem, we shall also need two lemmas from [19] that extend to the metaplectic group. The first lema is the metaplectic version of Lemma 3.7 of [19].…”

“…More precisely, we prove the following theorem. This result was proved for classical groups in [19], Theorem 13.2, assuming the cuspidal reducibility at 1 2 Z i.e. let ρ be an irreducible unitary cuspidal representation of the general linear group and σ a similar representation of the symplectic or the odd split special orthogonal group.…”

Composition series of the induced representations of SO(5) using intertwining operators

“…In the third section our main results are stated and proved. We determine composition series of the representations supported in the minimal parabolic subgroup, using rather new and powerful intertwining operator methods ( [7,8,10]), combined with the method of Jacquet modules ( [4,13,14]). In the last section we obtain the reducibility points of the representations with cuspidal support in the maximal parabolic subgroups.…”