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...
- Autores:
- Tipo de recurso:
- 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
- Rights
- restrictedAccess
- License
- http://purl.org/coar/access_right/c_16ec
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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 |
_version_ |
1814159252638400512 |