On the Muić conjecture--the irreducibility of the big theta lift
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912697320210432 |
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| author | Hanzer, Marcela |
| author_facet | Hanzer, Marcela |
| contents | Let $F$ be a non-archimedean local field of characteristic zero. We study theta correspondence for (complex) representations of symplectic--even orthogonal dual reductive pairs over $F;$ more specifically, the big theta lifts. We prove that, starting from a discrete series representation $π$ of a symplectic (even orthogonal group) over $F,$ its big theta lift $Θ(π)$ (as a representation of an even orthogonal (symplectic) group) if non-zero, is an irreducible representation, thus proving a conjecture of Muić. Building upon this result, we completely describe the situations in which the theta lifts of tempered representations are irreducible and when they are not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Muić conjecture--the irreducibility of the big theta lift Hanzer, Marcela Representation Theory 22E50, 11F27 Let $F$ be a non-archimedean local field of characteristic zero. We study theta correspondence for (complex) representations of symplectic--even orthogonal dual reductive pairs over $F;$ more specifically, the big theta lifts. We prove that, starting from a discrete series representation $π$ of a symplectic (even orthogonal group) over $F,$ its big theta lift $Θ(π)$ (as a representation of an even orthogonal (symplectic) group) if non-zero, is an irreducible representation, thus proving a conjecture of Muić. Building upon this result, we completely describe the situations in which the theta lifts of tempered representations are irreducible and when they are not. |
| title | On the Muić conjecture--the irreducibility of the big theta lift |
| topic | Representation Theory 22E50, 11F27 |
| url | https://arxiv.org/abs/2510.10389 |