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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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Інститут математики НАН України
2007
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147784 |
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irk-123456789-1477842019-02-17T01:26:35Z Antisymmetric Orbit Functions Klimyk, A. Patera, J. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147784 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| 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. |
| format |
Article |
| author |
Klimyk, A. Patera, J. |
| spellingShingle |
Klimyk, A. Patera, J. Antisymmetric Orbit Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Klimyk, A. Patera, J. |
| author_sort |
Klimyk, A. |
| title |
Antisymmetric Orbit Functions |
| title_short |
Antisymmetric Orbit Functions |
| title_full |
Antisymmetric Orbit Functions |
| title_fullStr |
Antisymmetric Orbit Functions |
| title_full_unstemmed |
Antisymmetric Orbit Functions |
| title_sort |
antisymmetric orbit functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147784 |
| citation_txt |
Antisymmetric Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT klimyka antisymmetricorbitfunctions AT pateraj antisymmetricorbitfunctions |
| first_indexed |
2023-05-20T17:28:31Z |
| last_indexed |
2023-05-20T17:28:31Z |
| _version_ |
1796153383191576576 |