Rank one reducibility for unitary groups
| Autor: | Marcela Hanzer |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Rank (linear algebra)
Mathematics::Number Theory General Mathematics Zero (complex analysis) Unitary state Dual (category theory) dual pairs unitary groups theta lifts nonarchimedean local field parabolic induction reducibility Combinatorics Unitary groups over non-archimedean fields reducibility of parabolic induction theta correspondence Filtration (mathematics) Mathematics::Representation Theory Representation (mathematics) Local field Symplectic geometry Mathematics |
| Zdroj: | Glasnik matematički Volume 46 Issue 1 |
| ISSN: | 0017-095X 1846-7989 |
| DOI: | 10.3336/gm.46.1.12 |
| Popis: | Let (G,G ' ) denote a dual reductive pair consisting of two unitary groups over a nonarchimedean local field of characteristic zero. We relate the reducibility of the parabolically induced representations of these two groups if the inducing data is cuspidal and related to each other by theta correspondence. We calculate theta lifts of the irreducible subquotients of these parabolically induced representations. To obtain these results, we explicitly calculate filtration of Jacquet modules of the appropriate Weil representation (as Kudla did for the orthogonal- symplectic dual pairs), but keeping in mind the explicit splittings of covers of these two unitary groups, also obtained by Kudla. |
| Databáze: | OpenAIRE |
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