New orthogonality relations for super-Jack polynomials and an associated Lassalle-Nekrasov correspondence (Q6149646)

The author studies orthogonality properties of super-Jack polynomials with respect to a bilinear form of the form \((p,q)\mapsto L_p(q)(0)\), where the \(L_p\)'s are quantum integrals of the deformed rational Calogero-Moser-Sutherland system. In [\textit{M. V. Feigin} et al., Commun. Math. Phys. 386, No. 1, 107--141 (2021; Zbl 1478.33006)], it was shown that there exists an intertwining relation between quantum integrals of deformed Calogero-Moser-Sutherland operators of trigonometric and rational harmonic type. This leads to a correspondence between joint eigenfunctions of these two integrable systems. As a consequence of the results of the present paper one obtains that this correspondence is isometric.