Antisymmetric Orbit Functions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Antisymmetric Orbit Functions
|
|
| Creator |
Klimyk, A.
Patera, J. |
|
| 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.
|
|
| Date |
2019-02-16T08:08:46Z
2019-02-16T08:08:46Z 2007 |
|
| Type |
Article
|
|
| Identifier |
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 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|