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

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Date
2016
Author
Caro-Lopera F.J.

Citación

       
TY - GEN T1 - The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator AU - Caro-Lopera F.J. Y1 - 2016 UR - http://hdl.handle.net/11407/3156 PB - Pushpa Publishing House AB - ER - @misc{11407_3156, author = {Caro-Lopera F.J.}, title = {The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator}, year = {2016}, abstract = {}, url = {http://hdl.handle.net/11407/3156} }RT Generic T1 The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator A1 Caro-Lopera F.J. YR 2016 LK http://hdl.handle.net/11407/3156 PB Pushpa Publishing House AB OL Spanish (121)
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Abstract
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). © 2016 Pushpa Publishing House, Allahabad, India.
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http://hdl.handle.net/11407/3156
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