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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| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146452 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1464522019-02-10T01:25:47Z Orbit Functions Klimyk, A. Patera, J. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146452 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Klimyk, A. Patera, J. |
| spellingShingle |
Klimyk, A. Patera, J. Orbit Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Klimyk, A. Patera, J. |
| author_sort |
Klimyk, A. |
| title |
Orbit Functions |
| title_short |
Orbit Functions |
| title_full |
Orbit Functions |
| title_fullStr |
Orbit Functions |
| title_full_unstemmed |
Orbit Functions |
| title_sort |
orbit functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146452 |
| citation_txt |
Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT klimyka orbitfunctions AT pateraj orbitfunctions |
| first_indexed |
2023-05-20T17:24:48Z |
| last_indexed |
2023-05-20T17:24:48Z |
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1796153240870453248 |