Zero-Eigenvalue Eigenfunctions for Differences of Elliptic Relativistic Calogero–Moser Hamiltonians

Letting $A_l(x)$ denote the commuting analytic difference operators of elliptic relativistic Calogero–Moser type, we present and study zero-eigenvalue eigenfunctions for the operators $A_l(x)-A_l(-y)$ ($l=1,2,\dots,N$, $x,y\in\mathbb C^N$) The eigenfunctions are products of elliptic gamma functions. They are invariant under permutations of $x_1,\dots,x_N$ and $y_1,\dots,y_N$ and under interchange of the step-size parameters.