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- W4283396072 abstract "Let $G_n$ be an inner form of a general linear group over a non-Archimedean field. We fix an arbitrary irreducible representation $sigma$ of $G_n$. Lapid-M'inguez give a combinatorial criteria for the irreducibility of parabolic induction when the inducing data is of the form $pi boxtimes sigma$ when $pi$ is a segment representation. We show that their criteria can be used to define a full subcategory of the category of smooth representation of some $G_m$, on which the parabolic induction functor $tau mapsto tau times sigma$ is fully-faithful. A key ingredient of our proof for the fully-faithfulness is constructions of indecomposable representations of length 2. Such result for a special situation has been previously applied in proving the local non-tempered Gan-Gross-Prasad conjecture for non-Archimedean general linear groups. In this article, we apply the fully-faithful result to prove a certain big derivative arising from Jacquet functor satisfies the property that its socle is irreducible and has multiplicity one in the Jordan-Holder sequence of the big derivative." @default.
- W4283396072 created "2022-06-25" @default.
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- W4283396072 date "2022-06-22" @default.
- W4283396072 modified "2023-09-27" @default.
- W4283396072 title "On the product functor on inner forms of general linear group over a non-Archimedean local field" @default.
- W4283396072 doi "https://doi.org/10.48550/arxiv.2206.10928" @default.
- W4283396072 hasPublicationYear "2022" @default.
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