An algorithm for Aubert-Zelevinsky duality à la Mœglin-Waldspurger
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911719086882816 |
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| author | Lanard, Thomas Mínguez, Alberto |
| author_facet | Lanard, Thomas Mínguez, Alberto |
| contents | Let $F$ be a locally compact non-Archimedean field of characteristic $0$, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$. The goal of this paper is to give an explicit description of the Aubert-Zelevinsky duality for $G$ in terms of Langlands parameters. We present a new algorithm, inspired by the Moeglin-Waldspurger algorithm for $\mathrm{GL}_n(F)$, which computes the dual Langlands data in a recursive and combinatorial way. Our method is simple enough to be carried out by hand and provides a practical tool for explicit computations. Interestingly, the algorithm was discovered with the help of machine learning tools, guiding us toward patterns that led to its formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algorithm for Aubert-Zelevinsky duality à la Mœglin-Waldspurger Lanard, Thomas Mínguez, Alberto Representation Theory Number Theory Let $F$ be a locally compact non-Archimedean field of characteristic $0$, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$. The goal of this paper is to give an explicit description of the Aubert-Zelevinsky duality for $G$ in terms of Langlands parameters. We present a new algorithm, inspired by the Moeglin-Waldspurger algorithm for $\mathrm{GL}_n(F)$, which computes the dual Langlands data in a recursive and combinatorial way. Our method is simple enough to be carried out by hand and provides a practical tool for explicit computations. Interestingly, the algorithm was discovered with the help of machine learning tools, guiding us toward patterns that led to its formulation. |
| title | An algorithm for Aubert-Zelevinsky duality à la Mœglin-Waldspurger |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2509.13231 |