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Ruijsenaars wavefunctions as modular group matrix coefficients

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We give a description of the Hallnäs-Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element S ∈ S L ( 2 , Z ) acting on the Hilbert space of GL(2) quantum Teichmüller theory on the pun... ...