  In this paper we investigate the multivariate orthogonal polynomials based on
the theory of interacting Fock spaces. Our framework is on the same stream line
of the recent paper by Accardi, Barhoumi, and Dhahri \cite{ABD}. The
(classical) coordinate variables are decomposed into non-commuting (quantum)
operators called creation, annihilation, and preservation operators, in the
interacting Fock spaces. Getting the commutation relations, which follow from
the commuting property of the coordinate variables between themselves, we can
develop the reconstruction theory of the measure, namely the Favard's theorem.
We then further develop some related problems including the marginal
distributions and the rank theory of the Jacobi operators. We will see that the
deficiency rank of the Jacobi operator implies that the underlying measure is
supported on some algebraic surface and vice versa. We will provide with some
examples.
