  This is the first in a series of papers in which we describe explicit
structural properties of spaces of diagonal rectangular harmonic polynomials in
$k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as
some of there relations to areas such as Algebraic Combinatorics,
Representation Theory, Algebraic Geometry, Knot Theory, and Theoretical
Physics. Our global aim is to develop a unifying point of view for several
areas of research of the last two decades having to do with Macdonald
Polynomials Operator Theory, Diagonal Coinvariant Spaces, Rectangular-Catalan
Combinatorics, the Delta-Conjecture, Hilbert Scheme of Points in the Plane,
Khovanov-Rozansky Homology of $(m,n)$-Torus links, etc.
