Orbit Functions

Symmetry, Integrability and Geometry: Methods and Applications

关键词: orbit functions;    Coxeter-Dynkin diagram;    Weyl group;    orbits;    products of orbits;    orbit function transform;    finite orbit function transform;    Neumann boundary problem;    symmetric polynomials;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown