On the matrices of Clebsch-Gordan coefficients
In a space of any dimension, the group \(\mathrm{SU}(2)\) admits a unique irreducible representation (up to equivalence). Each irreducile representation can be described in a simple way by using a canonical basis. The tensor product of two irreducible representations can be decomposed into a sum of irreducible representations. The vectors of the canonical bases of the corresponding invariant subspaces are linear combinations of tensor products between the vectors of the canonical bases of the considered representations. The coefficients, depending on three parameters, are called Clebsch-Gordan coefficients. The Clebsch-Gordan matrices, obtained in a certain way by using these coefficients, form a canonical basis for an irreducible representation of \(\mathrm{SU}(2)\) in a space of matrices. The author presents some new results concerning these remarkable matrices. The Clebsch-Gordan matrices transforming according to an irreducible representation of dimensions 1 or 3 are analyzed in detail.
representations of \(\mathrm{SO}(3)\) and \(\mathrm{SU}(2)\)
scientific article; zbMATH DE number 6862422