Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group

• Дата: 2006
• Автори: Moody, R.V., Patera, J.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2006
• Назва видання: Symmetry, Integrability and Geometry: Methods and Applications
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/146091
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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.

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.