Fonction génératrice des facteurs isoscalaires des groupes unitaires. (English) Zbl 0535.22018
An approach to the calculation of coupling coefficients of the unitary groups is proposed. A new schematisation of the elements of the bases of the fundamental representations is introduced and is used to find the generating function of coupling coefficients in a Gelfand basis. This generating function enables the author to find one corresponding to SU(n) isoscalar factors. As an illustration of the method the special case \(n=2\) is considered in detail.
Reviewer: A.Boguš
MSC:
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 22C05 | Compact groups |
| 22E46 | Semisimple Lie groups and their representations |
