2007/02/12 by Anatoliy Klimyk, Jiri Patera · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Mathematical Theories and Applications #Mathematical Analysis and Transform Methods #math-ph #math.CA #math.MP
paper · pdf · doi:10.3842/sigma.2007.023
published as SIGMA 3 (2007), 023, 83 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2007/02/12 · openalex publication_date 2007/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space E n 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 E n . Antisymmetric orbit functions are solutions of the corresponding Laplace equation in E n , 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.