Orbit Functions
| dc.creator | Klimyk, Anatoliy | |
| dc.creator | Patera, Jiri | |
| dc.date | 2006-01-19 | |
| dc.date.accessioned | 2026-07-07T09:34:23Z | |
| dc.date.available | 2026-07-07T09:34:23Z | |
| dc.description | 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. | |
| dc.description | Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/math-ph/0601037 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0601037 | |
| dc.identifier | SIGMA 2 (2006), 006, 60 pages | |
| dc.identifier | doi:10.3842/SIGMA.2006.006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159473 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Orbit Functions | |
| dc.type | text |