Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915934047830016 |
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| author | Hazeltine, Alexander Lo, Chi-Heng |
| author_facet | Hazeltine, Alexander Lo, Chi-Heng |
| contents | We give an algorithm to compute the Pyasetskii involution for $\mathrm{Sp}_{2n}$, $\mathrm{SO}_{2n+1}$ and $\mathrm{O}_{2n}$. The algorithm is a combination of Moeglin-Waldspurger's algorithm for the Pyasetskii involution for $\mathrm{GL}_n$ ([MW86]) and Lanard-M${í}$nguez's algorithm for the Aubert-Zelevinsky involution of bad parity representations for classical groups ([LM25]). In particular, we give a geometric interpretation of the bad parity case of Lanard-M${í}$nguez's algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11049 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups Hazeltine, Alexander Lo, Chi-Heng Representation Theory Number Theory We give an algorithm to compute the Pyasetskii involution for $\mathrm{Sp}_{2n}$, $\mathrm{SO}_{2n+1}$ and $\mathrm{O}_{2n}$. The algorithm is a combination of Moeglin-Waldspurger's algorithm for the Pyasetskii involution for $\mathrm{GL}_n$ ([MW86]) and Lanard-M${í}$nguez's algorithm for the Aubert-Zelevinsky involution of bad parity representations for classical groups ([LM25]). In particular, we give a geometric interpretation of the bad parity case of Lanard-M${í}$nguez's algorithm. |
| title | Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2604.11049 |