Local newforms for generic representations of unramified even unitary groups I: Even conductor case
In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integer and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters. To do this, we use the local Gan–Gross...
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| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000027/type/journal_article |
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| author | Hiraku Atobe |
| author_facet | Hiraku Atobe |
| author_sort | Hiraku Atobe |
| collection | DOAJ |
| description | In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integer and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters. To do this, we use the local Gan–Gross–Prasad conjecture, the local Rankin–Selberg integrals and the local theta correspondence. |
| format | Article |
| id | doaj-art-9248d9a68fa648f1a886618803f3946f |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-9248d9a68fa648f1a886618803f3946f2025-02-03T04:49:58ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.2Local newforms for generic representations of unramified even unitary groups I: Even conductor caseHiraku Atobe0https://orcid.org/0009-0002-6728-221XDepartment of Mathematics, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan;In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integer and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters. To do this, we use the local Gan–Gross–Prasad conjecture, the local Rankin–Selberg integrals and the local theta correspondence.https://www.cambridge.org/core/product/identifier/S2050509425000027/type/journal_article22E5011S37 |
| spellingShingle | Hiraku Atobe Local newforms for generic representations of unramified even unitary groups I: Even conductor case Forum of Mathematics, Sigma 22E50 11S37 |
| title | Local newforms for generic representations of unramified even unitary groups I: Even conductor case |
| title_full | Local newforms for generic representations of unramified even unitary groups I: Even conductor case |
| title_fullStr | Local newforms for generic representations of unramified even unitary groups I: Even conductor case |
| title_full_unstemmed | Local newforms for generic representations of unramified even unitary groups I: Even conductor case |
| title_short | Local newforms for generic representations of unramified even unitary groups I: Even conductor case |
| title_sort | local newforms for generic representations of unramified even unitary groups i even conductor case |
| topic | 22E50 11S37 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000027/type/journal_article |
| work_keys_str_mv | AT hirakuatobe localnewformsforgenericrepresentationsofunramifiedevenunitarygroupsievenconductorcase |