Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group

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dc.creatorMoody, Robert V.
dc.creatorPatera, Jiri
dc.date2006-11-08
dc.date.accessioned2026-07-07T09:34:26Z
dc.date.available2026-07-07T09:34:26Z
dc.descriptionThe 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 $\check F$ of the affine Weyl group. The members of each family satisfy basic orthogonality relations when integrated over $\check F$ (continuous orthogonality). It is demonstrated that the functions also satisfy discrete orthogonality relations when summed up over a finite grid in $\check F$ (discrete orthogonality), arising as the set of points in $\check F$ representing the conjugacy classes of elements of a finite Abelian subgroup of the maximal torus $\mathbb T$. The characters of the centre $Z$ of the Lie group allow one to split functions $f$ on $\check F$ 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.
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/0611020
dc.identifierhttp://arxiv.org/abs/math-ph/0611020
dc.identifierSIGMA 2 (2006), 076, 14 pages
dc.identifierdoi:10.3842/SIGMA.2006.076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159491
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.titleOrthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
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