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arXiv · 2306.09536

On two definitions of wave-front sets for $p$-adic groups

Cheng-Chiang Tsai
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Abstract

The wave-front set for an irreducible admissible representation of a $p$-adic reductive group is the set of maximal nilpotent orbits which appear in the local character expansion. By M\oe glin-Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are non-zero. However, in the literature there are two versions commonly used, one defining maximality using analytic closure and the other using Zariski closure. We show that these two definitions are non-equivalent for $G=Sp_4$.

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Cheng-Chiang Tsai. 2023-06-15. On two definitions of wave-front sets for $p$-adic groups. https://doi.org/10.2140/ant.2025.19.2471

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