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

Tsai, Cheng-Chiang

doi:10.2140/ant.2025.19.2471

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

Cheng-Chiang Tsai

Vol. 19 (2025), No. 12, 2471–2480

DOI: 10.2140/ant.2025.19.2471

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 a result of Mœglin and Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are nonzero. 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 inequivalent for $G = {Sp}_{4}$ .

Keywords

wave-front sets, $p$-adic groups

Mathematical Subject Classification

Primary: 22E35

Secondary: 11F30, 22E50

Milestones

Received: 15 April 2024

Revised: 23 August 2024

Accepted: 21 October 2024

Published: 20 October 2025

Authors

Cheng-Chiang Tsai
Institute of Mathematics Academia Sinica Taipei Taiwan	Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung Taiwan	Department of Mathematics National Taiwan University Taipei Taiwan

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Vol. 19, No. 12, 2025