Equivalence of the super Lax and local Dunkl operators for Calogero-like models

Abstract

Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax operators for the Calogero and Sutherland models can be expressed in terms of the supercharges and so called local Dunkl operators constructed in our recent paper with M. Ioffe. Several important relations involving Lax matrices and Hamiltonians of the Calogero and Sutherland models are easily derived from the properties of Dunkl operators.