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arXiv · 2607.07512

Aubert duality and co-tempered Langlands data

Nans Bonnel
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Abstract

Let $F$ be a non-archimedean local field of characteristic 0, and let $G$ be either $\mathrm{Sp}_{2n}(F)$ or $\mathrm{SO}_{2n+1}(F)$. We introduce a new algorithm to compute the Aubert dual at the level of Langlands data. This algorithm acts as the dual to the recent Lanard-Mínguez algorithm. It fundamentally differs in two ways: it follows a bottom-up approach rather than a top-down one, and its internal computations strictly preserve the temperedness of the representations. Consequently, this approach naturally yields a new constructive characterization of co-tempered representations. By operating exclusively within the realm of tempered data, this algorithm enables inductive proofs of new properties for co-tempered representations. In particular, we provide a precise description of their tempered components and establish an explicit duality formula for a large class of tempered representations.

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Nans Bonnel. 2026-07-15. Aubert duality and co-tempered Langlands data. https://arxiv.org/abs/2607.07512

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