Multilinear Hankel forms of higher order and orthogonal polynomials

The theory of bilinear Hankel forms of higher order (or higher weight) initiated in [12] is extended to the multilinear case.We study multilinear forms appearing in the decomposition of tensor products of function spaces on the disc with respect to a weighted action of the MÎbius group.We obtain a trace ideal criterion for these forms, and study discrete and continuous systems of orthogonal polynomials in several variables connected with the decomposition.Some of these polynomials are related to spherical harmonics.