Wei Zhang's Arithmetic Fundamental Lemma for unitary group elements
Wei Zhang's Arithmetic Fundamental Lemma for unitary group elements
Let be the relevant symmetric space, let be the unitary group attached to the odd hermitian form, and let , , and denote the transfer factor, the derivative of the orbital integral, and the intersection number. Let be regular semi-simple and matching an element . Assume either or that is artinian. Arithmetic Fundamental Lemma. Then
This is the group version of the Arithmetic Fundamental Lemma attributed to Wei Zhang. The surrounding discussion explains that the orbital integral itself vanishes on the nonsplit unitary side; no general resolution is stated in the source.
Sources & referencesView supporting material
Primary source
Andreas Mihatsch, “Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma”, arXiv:1611.06520 (2019).
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