التفاصيل البيبلوغرافية
| العنوان: |
Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group |
| المؤلفون: |
Robert V. Moody, Jiri Patera |
| المصدر: |
Symmetry, Integrability and Geometry: Methods and Applications, Vol 2, p 076 (2006) |
| بيانات النشر: |
National Academy of Science of Ukraine |
| سنة النشر: |
2006 |
| المجموعة: |
Directory of Open Access Journals: DOAJ Articles |
| مصطلحات موضوعية: |
orbit functions, Weyl group, semisimple Lie group, continuous orthogonality, discrete orthogonality, Mathematics, QA1-939 |
| الوصف: |
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 $f=f_1+cdots+f_c$, 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. |
| نوع الوثيقة: |
article in journal/newspaper |
| اللغة: |
English |
| تدمد: |
1815-0659 |
| Relation: |
http://www.emis.de/journals/SIGMA/2006/Paper076/; https://doaj.org/toc/1815-0659; https://doaj.org/article/eda4607dd3d2462fa544fdf1cc931584 |
| الاتاحة: |
https://doaj.org/article/eda4607dd3d2462fa544fdf1cc931584 |
| رقم الانضمام: |
edsbas.983AC997 |
| قاعدة البيانات: |
BASE |
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