Author:
Li Chao,Rapoport Michael,Zhang Wei
Abstract
AbstractWe 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 $$\textrm{U} (1)\times \textrm{U} (2)$$
U
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1
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U
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2
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Funder
Directorate for Mathematical and Physical Sciences
Simons Foundation
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
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