Abstract
We give three formulas for meromorphic eigenfunctions (scatteringstates) of Sutherland‘sintegrable N-body Schrödinger operators and their generalizations.The first is an explicit computation of the Etingof–Kirillov tracesof intertwining operators, the second an integral representationof hypergeometric type, and the third is a formula of Bethe ansatz type.The last two formulas are degenerations of elliptic formulasobtained previously in connection with theKnizhnik–Zamolodchikov–Bernardequation. The Bethe ansatz formulas in the elliptic case are reviewed and discussed in more detail here: Eigenfunctionsare parametrized by a ‘Hermite–Bethe’ variety, a generalizationof the spectral variety of the Lamé operator.We also give the q-deformed version of ourfirst formula. In the scalar slN case, this gives common eigenfunctionsof the commuting Macdonald–Rujsenaars difference operators.
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FELDER, G., VARCHENKO, A. Three formulas for eigenfunctions of integrable Schrödinger operators. Compositio Mathematica 107, 143–175 (1997). https://doi.org/10.1023/A:1000138423050
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DOI: https://doi.org/10.1023/A:1000138423050