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

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

## Resumen

© 2016 Pushpa Publishing House, Allahabad, India. 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 required solution demanded the construction of a new basis, in certain subspace, which can be written in a triangular array of ρ (ρ + 1) 2 non-negative integers (ρ ≤ τ), the method also provides some useful checking rules for the correctness of the tables. However, a counterexample for a recursion method is provided, going against the old conjecture that Davis’ polynomials can be computed recurrently as James’ zonal polynomials (James [7]). Given that the method is defined for the eigenvalues of the implied positive definite matrices, the idea of the paper holds naturally for invariant polynomials under real normed division algebras (real, complex, quaternions and octonions).
Idioma original Inglés estadounidense 1265-1288 24 Far East Journal of Mathematical Sciences 100 8 Publicada - 1 oct 2016