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

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Abstract

Letting Al(x) denote the commuting analytic difference operators of elliptic relativistic Calogero-Moser type, we present and study zero-eigenvalue eigenfunctions for the operators Al(x) − Al(−y) (with l = 1, 2,..., N and x, y ∈ N). The eigenfunctions are products of elliptic gamma functions. They are invariant under permutations of x1,..., xN and y1,..., yN and under interchange of the step-size parameters.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 31–41, January, 2006.

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Ruijsenaars, S.N.M. Zero-Eigenvalue Eigenfunctions for Differences of Elliptic Relativistic Calogero-Moser Hamiltonians. Theor Math Phys 146, 25–33 (2006). https://doi.org/10.1007/s11232-006-0003-y

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Keywords

  • relativistic Calogero-Moser systems
  • joint eigenfunctions
  • elliptic functional equations
  • elliptic gamma function