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[en] We describe the correspondence of the Matsuo–Cherednik type between the quantum n-body Ruijsenaars–Schneider model and the quantum Knizhnik–Zamolodchikov equations related to supergroup . The spectrum of the Ruijsenaars–Schneider Hamiltonians is shown to be independent of the -grading for a fixed value of , so that different qKZ systems of equations lead to the same n-body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical n-body Ruijsenaars–Schneider model and the supersymmetric quantum spin chains on n sites.