$C^\ast$-blocks and crossed products for classical $p$-adic groups
| العنوان: | $C^\ast$-blocks and crossed products for classical $p$-adic groups |
|---|---|
| المؤلفون: | Alexandre Afgoustidis, Anne-Marie Aubert |
| المساهمون: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP) |
| المصدر: | International Mathematics Research Notices International Mathematics Research Notices, In press, ⟨10.1093/imrn/rnab163⟩ International Mathematics Research Notices, Oxford University Press (OUP), In press, ⟨10.1093/imrn/rnab163⟩ |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Pure mathematics, General Mathematics, 010102 general mathematics, Mathematics - Operator Algebras, 01 natural sciences, 0103 physical sciences, FOS: Mathematics, 22E50, 22D25, 010307 mathematical physics, Representation Theory (math.RT), 0101 mathematics, [MATH]Mathematics [math], Operator Algebras (math.OA), Mathematics - Representation Theory, Mathematics |
| الوصف: | Let $G$ be a real or $p$-adic reductive group. We consider the tempered dual of $G$, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple geometric structure which encodes the reducibility of induced representations. For $p$-adic groups, each connected component of the tempered dual comes with a compact torus equipped with a finite group action, and we prove that a version of Wassermann's theorem holds true under a certain geometric assumption on the structure of stabilizers for that action. We then focus on the case where $G$ is a quasi-split symplectic, orthogonal or unitary group, and explicitly determine the connected components for which the geometric assumption is satisfied. Version 3 (40 pages), to appear in IMRN |
| اللغة: | English |
| تدمد: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rnab163⟩ |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fcb83ce1671d082536507bdca0d48ed http://arxiv.org/abs/2002.12864 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....2fcb83ce1671d082536507bdca0d48ed |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10737928 16870247 |
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| DOI: | 10.1093/imrn/rnab163⟩ |