An algorithm for Aubert-Zelevinsky duality à la Mœglin-Waldspurger

2025/09/16 by Thomas Lanard, Alberto Mínguez, Lanard, Thomas +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2509.13231

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

Let F be a locally compact non-Archimedean field of characteristic 0, and let G be either the split special orthogonal group SO_2n+1(F) or the symplectic group Sp_2n(F). The goal of this paper is to give an explicit description of the Aubert-Zelevinsky duality for G in terms of Langlands parameters. We present a new algorithm, inspired by the Moeglin-Waldspurger algorithm for GL_n(F), which computes the dual Langlands data in a recursive and combinatorial way. Our method is simple enough to be carried out by hand and provides a practical tool for explicit computations. Interestingly, the algorithm was discovered with the help of machine learning tools, guiding us toward patterns that led to its formulation.

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