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

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$\tilde{A}­$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$\tilde{A}­$nguez's algorithm.

29 pages, comments are welcome