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Article: On the Product Functor on Inner forms of the General Linear Group Over A Non-Archimedean Local Field
Title | On the Product Functor on Inner forms of the General Linear Group Over A Non-Archimedean Local Field |
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Authors | |
Issue Date | 2-May-2024 |
Publisher | Springer |
Citation | Transformation Groups, 2024 How to Cite? |
Abstract | Let Gn be an inner form of a general linear group over a non-Archimedean local field. We fix an arbitrary irreducible representation σ of Gn. Building on the work of Lapid-Mínguez on the irreducibility of parabolic inductions, we show how to define a full subcategory of the category of smooth representations of some Gm, on which the parabolic induction functor τ↦τ×σ 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-Hölder sequence of the big derivative. |
Persistent Identifier | http://hdl.handle.net/10722/347764 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.844 |
DC Field | Value | Language |
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dc.contributor.author | Chan, Kei Yuen | - |
dc.date.accessioned | 2024-09-28T00:30:25Z | - |
dc.date.available | 2024-09-28T00:30:25Z | - |
dc.date.issued | 2024-05-02 | - |
dc.identifier.citation | Transformation Groups, 2024 | - |
dc.identifier.issn | 1083-4362 | - |
dc.identifier.uri | http://hdl.handle.net/10722/347764 | - |
dc.description.abstract | <p>Let Gn be an inner form of a general linear group over a non-Archimedean local field. We fix an arbitrary irreducible representation σ of Gn. Building on the work of Lapid-Mínguez on the irreducibility of parabolic inductions, we show how to define a full subcategory of the category of smooth representations of some Gm, on which the parabolic induction functor τ↦τ×σ 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-Hölder sequence of the big derivative.<br></p> | - |
dc.language | eng | - |
dc.publisher | Springer | - |
dc.relation.ispartof | Transformation Groups | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | On the Product Functor on Inner forms of the General Linear Group Over A Non-Archimedean Local Field | - |
dc.type | Article | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1007/s00031-024-09861-4 | - |
dc.identifier.scopus | eid_2-s2.0-85191999417 | - |
dc.identifier.eissn | 1531-586X | - |
dc.identifier.issnl | 1083-4362 | - |