Antisymmetric Orbit Functions
In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space En are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of s...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147784 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Antisymmetric Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862543832136024064 |
|---|---|
| author | Klimyk, A. Patera, J. |
| author_facet | Klimyk, A. Patera, J. |
| citation_txt | Antisymmetric Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space En are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group G of rank n. Up to a sign, values of antisymmetric 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. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in En, vanishing on the boundary of the fundamental domain F. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group G. They also determine a transform on a finite set of points of F (the discrete antisymmetric orbit function transform). Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.
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| first_indexed | 2025-11-24T23:52:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147784 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T23:52:53Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Klimyk, A. Patera, J. 2019-02-16T08:08:46Z 2019-02-16T08:08:46Z 2007 Antisymmetric Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33-02; 33E99; 42B99; 42C15; 58C40 https://nasplib.isofts.kiev.ua/handle/123456789/147784 In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space En are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group G of rank n. Up to a sign, values of antisymmetric 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. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in En, vanishing on the boundary of the fundamental domain F. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group G. They also determine a transform on a finite set of points of F (the discrete antisymmetric orbit function transform). Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given. The first author (AK) acknowledges CRM of University of Montreal for hospitality when this paper was under preparation. His research was partially supported by Grant 10.01/015 of the State Foundation of Fundamental Research of Ukraine. We are grateful for partial support for this work to the National Research Council of Canada, MITACS, the MIND Institute of Costa Mesa, California, and Lockheed Martin, Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Antisymmetric Orbit Functions Article published earlier |
| spellingShingle | Antisymmetric Orbit Functions Klimyk, A. Patera, J. |
| title | Antisymmetric Orbit Functions |
| title_full | Antisymmetric Orbit Functions |
| title_fullStr | Antisymmetric Orbit Functions |
| title_full_unstemmed | Antisymmetric Orbit Functions |
| title_short | Antisymmetric Orbit Functions |
| title_sort | antisymmetric orbit functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147784 |
| work_keys_str_mv | AT klimyka antisymmetricorbitfunctions AT pateraj antisymmetricorbitfunctions |