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arXiv · 2604.11049

Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups

Alexander Hazeltine·Chi-Heng Lo
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Abstract

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${\'i}$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${\'i}$nguez's algorithm.

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Alexander Hazeltine, Chi-Heng Lo. 2026-04-13. Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups. https://arxiv.org/abs/2604.11049

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