Geodesic
Zero-Eigenvalue Eigenfunctions for Differences of Elliptic Relativistic Calogero--Moser Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 31-41

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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.
Keywords: relativistic Calogero-Moser systems, joint eigenfunctions, elliptic functional equations, elliptic gamma function. 
@article{TMF_2006_146_1_a2,
     author = {S. Ruijsenaars},
     title = {Zero-Eigenvalue {Eigenfunctions} for {Differences} of {Elliptic} {Relativistic} {Calogero--Moser} {Hamiltonians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {31--41},
     publisher = {mathdoc},
     volume = {146},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a2/}
}
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S. Ruijsenaars. Zero-Eigenvalue Eigenfunctions for Differences of Elliptic Relativistic Calogero--Moser Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 31-41. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a2/