2008/01/05 by Anatoliy Klimyk, Anatoliy U. Klimyk, Jiri Patera · 3 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #math-ph #math.CA #math.MP
paper · pdf · doi:10.3842/sigma.2008.002
published as SIGMA 4 (2008), 002, 57 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2008/01/05 · openalex publication_date 2008/01/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We review and further develop the theory of E-orbit functions. They are functions on the Euclidean space E n obtained from the multivariate exponential function by symmetrization by means of an even part W e 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 W aff e 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 F e of the group W aff e (the discrete E-orbit function transform).