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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.09033 |
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| _version_ | 1866914153209266176 |
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| author | Tiwari, Ekta |
| author_facet | Tiwari, Ekta |
| contents | Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this article, we determine the branching rules for all irreducible supercuspidal representations of $G$, that is, we explicitly describe their decomposition upon restriction to a fixed maximal compact subgroup $\mathcal{K}$ in terms of irreducible representations of $\mathcal{K}$. We also present two applications of these decompositions, which verify two new conjectures in the literature for $G$. Together with the results from a previous paper by the author, this article completes the description of the branching rules for all irreducible smooth representations of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branching rules for irreducible supercuspidal representations of unramified $\mathrm{U}(1,1)$ Tiwari, Ekta Representation Theory Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this article, we determine the branching rules for all irreducible supercuspidal representations of $G$, that is, we explicitly describe their decomposition upon restriction to a fixed maximal compact subgroup $\mathcal{K}$ in terms of irreducible representations of $\mathcal{K}$. We also present two applications of these decompositions, which verify two new conjectures in the literature for $G$. Together with the results from a previous paper by the author, this article completes the description of the branching rules for all irreducible smooth representations of $G$. |
| title | Branching rules for irreducible supercuspidal representations of unramified $\mathrm{U}(1,1)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2511.09033 |