  In the previous works \cite{N46,N47} authors have defined the oscillator-like
system that associated with the two variable Chebyshev-Koornwinder polynomials.
We call this system the generalized Chebyshev - Koornwinder oscillator. In this
paper we study the properties of infinite-dimensional Lie algebra that is
analogous to the Heisenberg algebra for the Chebyshev - Koornwinder oscillator.
We construct the exact irreducible representation of this algebra in a Hilbert
space $\mathcal{H}$ of functions that are defined on a region which bounded by
the Steiner hypocycloid. The functions are square-integrable with respect to
the orthogonality measure for the Chebyshev - Koornwinder polynomials and these
polynomials form an orthonormalized basis in the space $\mathcal{H}$. The
generalized oscillator which is studied in the work can be considered as the
simplest nontrivial example of multiboson quantum system that is composed of
three interacting oscillators.
