Antisymmetric Orbit Functions

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dc.creatorKlimyk, Anatoliy
dc.creatorPatera, Jiri
dc.date2007-02-12
dc.date.accessioned2026-07-07T09:34:27Z
dc.date.available2026-07-07T09:34:27Z
dc.descriptionIn 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0702040
dc.identifierhttp://arxiv.org/abs/math-ph/0702040
dc.identifierSIGMA 3 (2007), 023, 83 pages
dc.identifierdoi:10.3842/SIGMA.2007.023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159498
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.titleAntisymmetric Orbit Functions
dc.typetext

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