LAUSR

Abstract 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 G L ( N | M ) . The spectrum of the Ruijsenaars–Schneider Hamiltonians is shown to be independent of the Z 2 -grading for a fixed value of N + M , so that N + M + 1 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 G L ( N | M ) quantum spin chains on n sites.