The invariant polynomials characterizing U(n) tensor operators 〈p, q,…, q, 0,…, 0〉 having maximal null space

AbstractWe make use of the “path sum” function to prove that the family of stretched operator functions characterized by the operator irrep labels 〈p,q,…,q, 0,…, 0〉 satisfy a pair of general difference equations. This family of functions is a generalization of Milne's 〈p,q,…,q, 0,〉 functions for U(n) and Biedenharn and Louck's 〈p,q, 0〉 functions for U(3). The fact that this family of stretched operator functions are polynomials follows from a detailed study of their symmetries and zeros. As a further application of our general difference equations and symmetry properties we give an explicit formula for the polynomials characterized by the operator irrep labels 〈p, 1, 0,…, 0〉