Orbit Functions
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space En 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....
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146452 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862529273694257152 |
|---|---|
| author | Klimyk, A. Patera, J. |
| author_facet | Klimyk, A. Patera, J. |
| citation_txt | Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space En 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 En. Orbit functions are solutions of the corresponding Laplace equation in En, 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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| first_indexed | 2025-11-24T02:39:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146452 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T02:39:20Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Klimyk, A. Patera, J. 2019-02-09T17:23:26Z 2019-02-09T17:23:26Z 2006 Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33-02; 33E99; 42C15; 58C40 https://nasplib.isofts.kiev.ua/handle/123456789/146452 In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space En 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 En. Orbit functions are solutions of the corresponding Laplace equation in En, 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. The first author (AK) acknowledges CRM of University of Montreal for hospitality when this paper was under preparation. We are grateful for partial support for this work to the National Research Council of Canada and to MITACS. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orbit Functions Article published earlier |
| spellingShingle | Orbit Functions Klimyk, A. Patera, J. |
| title | Orbit Functions |
| title_full | Orbit Functions |
| title_fullStr | Orbit Functions |
| title_full_unstemmed | Orbit Functions |
| title_short | Orbit Functions |
| title_sort | orbit functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146452 |
| work_keys_str_mv | AT klimyka orbitfunctions AT pateraj orbitfunctions |