Supersymmetric extension of qKZ-Ruijsenaars correspondence

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 GL(N vertical bar 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 GL(N vertical bar M) quantum spin chains on n sites. (C) 2018 The Author(s). Published by Elsevier B.V.