An element [Φ] ∈ Gr n (H + , F) of the Grassmannian of n-dimensional subspaces of the Hardy space H + = H 2 , extended over the field F = C(x 1 , . . . , x n ), may be associated to any polynomial basis, labelled by partitions λ, provide an analog of Jacobi's bi-alternant formula, defining a generalization of Schur polynomials. Applying the recursion relations satisfied by the polynomial system φ to the analog {h (0) i } of the complete symmetric functions generates a doubly infinite matrix h (j) * Work of J.H. supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds Québecois de la recherche sur la nature et les technologies (FQRNT).