Classification of $\mathrm{GL}_{n}(\mathbb{C})$-Representations Distinguished by $\mathrm{GL}_n(\mathbb{R})$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912266512760832 |
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| author | Pattanayak, Basudev Wu, Kaidi Zhang, Hongfeng |
| author_facet | Pattanayak, Basudev Wu, Kaidi Zhang, Hongfeng |
| contents | This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for each such $\mathrm{GL}_n(\mathbb{R})$-distinguished representation, we explicitly construct the associated period and prove its non-vanishing on the distinguished minimal $K$-type. Furthermore, we offer some applications to the branching problem using theta correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of $\mathrm{GL}_{n}(\mathbb{C})$-Representations Distinguished by $\mathrm{GL}_n(\mathbb{R})$ Pattanayak, Basudev Wu, Kaidi Zhang, Hongfeng Representation Theory 22E50, 11F70 This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for each such $\mathrm{GL}_n(\mathbb{R})$-distinguished representation, we explicitly construct the associated period and prove its non-vanishing on the distinguished minimal $K$-type. Furthermore, we offer some applications to the branching problem using theta correspondence. |
| title | Classification of $\mathrm{GL}_{n}(\mathbb{C})$-Representations Distinguished by $\mathrm{GL}_n(\mathbb{R})$ |
| topic | Representation Theory 22E50, 11F70 |
| url | https://arxiv.org/abs/2501.14449 |