2006/01/19 by Anatoliy Klimyk, Jiri Patera · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods #math-ph #math.CA #math.MP
paper · pdf · doi:10.3842/sigma.2006.006
published as SIGMA 2 (2006), 006, 60 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2006/01/19 · openalex publication_date 2006/01/19 · arxiv updated 2009/12/01 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/28
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E n 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 E n . Orbit functions are solutions of the corresponding Laplace equation in E n , 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.