Orbit Functions

In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described....
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Anatoliy Klimyk [verfasserIn] Jiri Patera [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2006

Schlagwörter:	orbit functions Coxeter-Dynkin diagram Weyl group orbits products of orbits orbit function transform finite orbit function transform Neumann boundary problem symmetric polynomials

Übergeordnetes Werk:	In: Symmetry, Integrability and Geometry: Methods and Applications - National Academy of Science of Ukraine, 2005, 2, p 006(2006)
Übergeordnetes Werk:	volume:2, p 006 ; year:2006

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ053437578

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spelling	(DE-627)DOAJ053437578 (DE-599)DOAJb6fbf3f4d39b4f3db0f3598d163c3284 DE-627 ger DE-627 rakwb eng QA1-939 Anatoliy Klimyk verfasserin aut Orbit Functions 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points. orbit functions Coxeter-Dynkin diagram Weyl group orbits products of orbits orbit function transform finite orbit function transform Neumann boundary problem symmetric polynomials Mathematics Jiri Patera verfasserin aut In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 2, p 006(2006) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:2, p 006 year:2006 https://doaj.org/article/b6fbf3f4d39b4f3db0f3598d163c3284 kostenfrei http://www.emis.de/journals/SIGMA/2006/Paper006/ kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2, p 006 2006
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allfieldsSound	(DE-627)DOAJ053437578 (DE-599)DOAJb6fbf3f4d39b4f3db0f3598d163c3284 DE-627 ger DE-627 rakwb eng QA1-939 Anatoliy Klimyk verfasserin aut Orbit Functions 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points. orbit functions Coxeter-Dynkin diagram Weyl group orbits products of orbits orbit function transform finite orbit function transform Neumann boundary problem symmetric polynomials Mathematics Jiri Patera verfasserin aut In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 2, p 006(2006) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:2, p 006 year:2006 https://doaj.org/article/b6fbf3f4d39b4f3db0f3598d163c3284 kostenfrei http://www.emis.de/journals/SIGMA/2006/Paper006/ kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2, p 006 2006
language	English
source	In Symmetry, Integrability and Geometry: Methods and Applications 2, p 006(2006) volume:2, p 006 year:2006
sourceStr	In Symmetry, Integrability and Geometry: Methods and Applications 2, p 006(2006) volume:2, p 006 year:2006
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	orbit functions Coxeter-Dynkin diagram Weyl group orbits products of orbits orbit function transform finite orbit function transform Neumann boundary problem symmetric polynomials Mathematics
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container_title	Symmetry, Integrability and Geometry: Methods and Applications
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author	Anatoliy Klimyk
spellingShingle	Anatoliy Klimyk misc QA1-939 misc orbit functions misc Coxeter-Dynkin diagram misc Weyl group misc orbits misc products of orbits misc orbit function transform misc finite orbit function transform misc Neumann boundary problem misc symmetric polynomials misc Mathematics Orbit Functions
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topic_title	QA1-939 Orbit Functions orbit functions Coxeter-Dynkin diagram Weyl group orbits products of orbits orbit function transform finite orbit function transform Neumann boundary problem symmetric polynomials
topic	misc QA1-939 misc orbit functions misc Coxeter-Dynkin diagram misc Weyl group misc orbits misc products of orbits misc orbit function transform misc finite orbit function transform misc Neumann boundary problem misc symmetric polynomials misc Mathematics
topic_unstemmed	misc QA1-939 misc orbit functions misc Coxeter-Dynkin diagram misc Weyl group misc orbits misc products of orbits misc orbit function transform misc finite orbit function transform misc Neumann boundary problem misc symmetric polynomials misc Mathematics
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title_auth	Orbit Functions
abstract	In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points.
abstractGer	In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points.
abstract_unstemmed	In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points.
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