The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator

In this paper, we solve an open problem proposed by Davis in [3] about the construction of the invariant polynomials by using the Laplace-Beltrami operator. Until now, only a basis for the non-normalized polynomials is known, and the coefficients need to be collected in τ × τ array of integers. The...