2006/11/08 by Robert V. Moody, Jiri Patera · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Molecular spectroscopy and chirality #math-ph #math.CA #math.MP
paper · pdf · doi:10.3842/sigma.2006.076
published as SIGMA 2 (2006), 076, 14 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2006/11/08 · openalex publication_date 2006/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group G. Such functions can always be restricted without loss of information to a fundamental region F of the affine Weyl group. The members of each family satisfy basic orthogonality relations when integrated over F (continuous orthogonality). It is demonstrated that the functions also satisfy discrete orthogonality relations when summed up over a finite grid in F (discrete orthogonality), arising as the set of points in F representing the conjugacy classes of elements of a finite Abelian subgroup of the maximal torus T. The characters of the centre Z of the Lie group allow one to split functions f on F into a sum f = f 1 + + f c , where c is the order of Z, and where the component functions f k decompose into the series of C-, or S-, or E-functions from one congruence class only.