  We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang.
This relies on a recursive algorithm which allows, under certain conditions, to
reduce the AFL identity in question to an AFL identity in lower dimension. The
main ingredient for this reduction is a comparison isomorphism between
different moduli problems of PEL-type for p-divisible groups. The construction
of this comparison isomorphism is based on the theory of relative displays and
frames, as developed by Tobias Ahsendorf, Eike Lau and Thomas Zink.
