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E-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, 2008, том 4
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E-Orbit Functions
Інший ID:
2000 Mathematics Subject Classification: 33-02; 33E99; 42B99; 42C15; 58C40
Посилання:
E-Orbit Functions / A.U. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ.
Підтримка:
The first author acknowledges CRM of University of Montreal for hospitality when this paper was under preparation. We are grateful for partial support for this work from the National Science and Engineering Research Council of Canada, MITACS, the MIND Institute of Costa Mesa, California, and Lockheed Martin, Canada.
Дата:
2008
Переглядів:
533
Завантажень:
155
Анотація:
We review and further develop the theory of E-orbit functions. They are functions on the Euclidean space En obtained from the multivariate exponential function by symmetrization by means of an even part We of a Weyl group W, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. They are closely related to symmetric and antisymmetric orbit functions which are received from exponential functions by symmetrization and antisymmetrization procedure by means of a Weyl group W. The E-orbit functions, determined by integral parameters, are invariant with respect to even part Weaff of the affine Weyl group corresponding to W. The E-orbit functions determine a symmetrized Fourier transform, where these functions serve as a kernel of the transform. They also determine a transform on a finite set of points of the fundamental domain Fe of the group Weaff (the discrete E-orbit function transform).
