Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hn−p,n−q, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies for all p, q. Adapting an argument of Chern, Hirzebruch, and Serre  in an obvious way, in this short note we observe that this “Serre symmetry” holds on all subsequent pages of the spectral sequence as well. The argument shows that an analogous statement holds for the Frölicher spectral sequence of an almost complex structure on a nilpotent real Lie group as considered by Cirici and Wilson in .
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