Arithmetic Fundamental Lemma for the spherical Hecke algebra

2023/05/23 by Chao Li, Li, Chao, Michael Rapoport +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2305.14465

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity conjecture on Hecke operators. Then we formulate the Arithmetic Fundamental Lemma conjecture for the spherical Hecke algebra. We also formulate a conjecture on the abundance of spherical Hecke functions with identically vanishing first derivative of orbital integrals. We prove these conjectures for the case U(1)× U(2).

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