a general scheme for construction of the generalized oscillator, i.e. oscillator-like algebra which is a Heisenberg algebra generalization that connected with the given system of orthogonal polynomials on the real axis [@N16].

In last time increased interest to different applications of orthogonal polynomials in several variables. For general results concerning such polynomials we refer the reader to the monographs [@N17; @N18]. We note also recent works [@N19; @N20], as well as earlier work on two-variable Krall - Schaefer polynomials [@N21] that associated with integrable systems on the spaces of constant curvature (see also [@N22; @N23]). In this regard, it is natural to extend the construction of the generalized oscillator connected with orthogonal polynomials in one variable to the case of polynomials of several variables. We start by considering a simple but non-trivial generalizations of the classical polynomials in one variable to the case of several variables. A wide class of such polynomials is connected with the root systems of Lie algebras [@N24]-[@N27].

One of the first works in this direction was the T. Koornwinder article [@N28], the main results of which were presented in [@N17] (see additional details in [@N29]-[@N31]). In this work [@N28] Koornwinder introduces orthogonal polynomials that are 