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Symmetry of Arthur parameters under Aubert involution

Dubravka Ban
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Abstract

We consider a nontempered $A$-parameter $ψ$ of $SO(2n+1, F)$ of a certain type and the base point representation $π$ in the $A$-packet of $ψ$. Let $\hatπ$ be the Aubert involution of $π$. We compute explicitly the Langlands data of $\hatπ$ and the $A$-parameter $\hatψ$ of $\hatπ$. We investigate whether $ψ$ and $\hatψ$ are symmetric. Although symmetry holds for large classes of parameters, it does not hold in general.

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Dubravka Ban. 2004-02-25. Symmetry of Arthur parameters under Aubert involution. https://arxiv.org/abs/math/0401261

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