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We present a basis of eigenvectors for the graph building operators actingalong the mirror channel of planar fishnet Feynman integrals in $d$-dimensions.The eigenvectors of a fishnet lattice of length $L$ depend on a set of $L$quantum numbers $(u_k,l_k)$, each associated with the rapidity and bound-stateindex of a lattice excitation. Each excitation is a particle in$(1+1)$-dimensions with $O(d)$ internal symmetry, and the wave-functions areformally constructed with a set of creation/annihilation operators that satisfythe corresponding Zamolodchikovs-Faddeev algebra. These properties are provedvia the representation - new to our knowledge - of the matrix elements of thefused R-matrix with $O(d)$ symmetry as integral operators on the functions oftwo spacetime points. The spectral decomposition of a fishnet integral weachieved can be applied to the computation of Basso-Dixon integrals in higherdimensions.

Mirror channel eigenvectors of the $d$-dimensional fishnets