Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group
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 fundamen...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146091 |
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| Zitieren: | Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group / R.V. Moody, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Moody, R.V. Patera, J. 2019-02-07T09:21:53Z 2019-02-07T09:21:53Z 2006 Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group / R.V. Moody, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 23 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C80; 17B10; 42C15 https://nasplib.isofts.kiev.ua/handle/123456789/146091 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 F of the affine Weyl group. The members of each family satisfy basic orthogonality relations when integrated over F (continuous orthogonality). It is demonstrated that the functions also satisfy discrete orthogonality relations when summed up over a finite grid in F (discrete orthogonality), arising as the set of points in F representing the conjugacy classes of elements of a finite Abelian subgroup of the maximal torus T. The characters of the centre Z of the Lie group allow one to split functions f on F into a sum f = f1 + ... + fc, where c is the order of Z, and where the component functions fk decompose into the series of C-, or S-, or E-functions from one congruence class only. Work supported in part by the Natural Sciences and Engineering Research Council of Canada, MITACS, M.I.N.D. Institute of Costa Mesa, Calif., and by Lockheed Martin Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group |
| spellingShingle |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group Moody, R.V. Patera, J. |
| title_short |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group |
| title_full |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group |
| title_fullStr |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group |
| title_full_unstemmed |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group |
| title_sort |
orthogonality within the families of c-, s-, and e-functions of any compact semisimple lie group |
| author |
Moody, R.V. Patera, J. |
| author_facet |
Moody, R.V. Patera, J. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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 F of the affine Weyl group. The members of each family satisfy basic orthogonality relations when integrated over F (continuous orthogonality). It is demonstrated that the functions also satisfy discrete orthogonality relations when summed up over a finite grid in F (discrete orthogonality), arising as the set of points in F representing the conjugacy classes of elements of a finite Abelian subgroup of the maximal torus T. The characters of the centre Z of the Lie group allow one to split functions f on F into a sum f = f1 + ... + fc, where c is the order of Z, and where the component functions fk decompose into the series of C-, or S-, or E-functions from one congruence class only.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146091 |
| citation_txt |
Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group / R.V. Moody, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 23 назв. — англ. |
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AT moodyrv orthogonalitywithinthefamiliesofcsandefunctionsofanycompactsemisimpleliegroup AT pateraj orthogonalitywithinthefamiliesofcsandefunctionsofanycompactsemisimpleliegroup |
| first_indexed |
2025-12-07T18:08:01Z |
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2025-12-07T18:08:01Z |
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1850873879380099072 |