Differential Operators and Weighted Isobaric Polynomials

Abstract

We characterize those sequences of weighted isobaric polynomials as defined in math.CO/0106213 which belong to the kernel of the linear operator $D_{11}-{\sum }_{j=1}^k{a}_j{t}_j{D}_{2j}-m{D}_2$, and we characterize those linear operators of this form in terms of the coefficients $a_j$ which have a non-zero kernel.

11 pages, 2 figures