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Orbit Functions
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Orbit Functions
Інший ID:
2000 Mathematics Subject Classification: 33-02; 33E99; 42C15; 58C40
Посилання:
Orbit Functions / A. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ.
Підтримка:
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.
Дата:
2006
Переглядів:
498
Завантажень:
203
Анотація:
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.
