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...

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Fecha de publicación:
2016
Institución:
Universidad de Medellín
Repositorio:
Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/3156
Acceso en línea:
http://hdl.handle.net/11407/3156
Palabra clave:
Invariant polynomials
Laplace-beltrami operator
Zonal polynomials
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restrictedAccess
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http://purl.org/coar/access_right/c_16ec
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spelling 2017-05-12T16:05:59Z2017-05-12T16:05:59Z20169720871http://hdl.handle.net/11407/315610.17654/MS100081265In 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.engPushpa Publishing Househttp://www.pphmj.com/abstract/10180.htmFar East Journal of Mathematical SciencesScopusInvariant polynomialsLaplace-beltrami operatorZonal polynomialsThe impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operatorArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/access_right/c_16ecCaro-Lopera, F.J., Department of Basic Sciences, University of Medellin, Medellin, ColombiaCaro-Lopera F.J.11407/3156oai:repository.udem.edu.co:11407/31562020-05-27 19:10:36.325Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co
dc.title.spa.fl_str_mv The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
title The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
spellingShingle The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
Invariant polynomials
Laplace-beltrami operator
Zonal polynomials
title_short The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
title_full The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
title_fullStr The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
title_full_unstemmed The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
title_sort The impossibility of a recurrence construction of the invariant polynomials by using the laplace-beltrami operator
dc.contributor.affiliation.spa.fl_str_mv Caro-Lopera, F.J., Department of Basic Sciences, University of Medellin, Medellin, Colombia
dc.subject.spa.fl_str_mv Invariant polynomials
Laplace-beltrami operator
Zonal polynomials
topic Invariant polynomials
Laplace-beltrami operator
Zonal polynomials
description 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.
publishDate 2016
dc.date.created.none.fl_str_mv 2016
dc.date.accessioned.none.fl_str_mv 2017-05-12T16:05:59Z
dc.date.available.none.fl_str_mv 2017-05-12T16:05:59Z
dc.type.eng.fl_str_mv Article
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 9720871
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/3156
dc.identifier.doi.none.fl_str_mv 10.17654/MS100081265
identifier_str_mv 9720871
10.17654/MS100081265
url http://hdl.handle.net/11407/3156
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv http://www.pphmj.com/abstract/10180.htm
dc.relation.ispartofes.spa.fl_str_mv Far East Journal of Mathematical Sciences
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/restrictedAccess
eu_rights_str_mv restrictedAccess
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv Pushpa Publishing House
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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