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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 076, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.076
(Mi sigma104)
 

This article is cited in 35 scientific papers (total in 35 papers)

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

Robert V. Moodya, Jiri Paterab

a Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada
b Centre de Recherches Mathématiques, Université de Montréal, C.P.6128-Centre ville, Montréal, H3C 3J7, Québec, Canada
References:
Abstract: 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 $\check F$ 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 $f=f_1+\dots+f_c$, 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.
Keywords: orbit functions; Weyl group; semisimple Lie group; continuous orthogonality; discrete orthogonality.
Received: October 30, 2006; Published online November 8, 2006
Bibliographic databases:
Document Type: Article
MSC: 33C80; 17B10; 42C15
Language: English
Citation: Robert V. Moody, Jiri Patera, “Orthogonality within the Families of $C$-, $S$-, and $E$-Functions of Any Compact Semisimple Lie Group”, SIGMA, 2 (2006), 076, 14 pp.
Citation in format AMSBIB
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\by Robert V.~Moody, Jiri Patera
\paper Orthogonality within the Families of $C$-, $S$-, and $E$-Functions of Any Compact Semisimple Lie Group
\jour SIGMA
\yr 2006
\vol 2
\papernumber 076
\totalpages 14
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  • This publication is cited in the following 35 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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