On the matrices of Clebsch-Gordan coefficients
type: Item
instance of: scholarly article
title: On the matrices of Clebsch-Gordan coefficients
zbMATH Open document ID: 1398.22015
DOI: 10.1134/S0037446617060088
author: Xianqiang Yang
published in: Siberian Mathematical Journal
publication date: 2018-04-20T00:00:00Z
review text: 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.
reviewed by: Nicolae Cotfas
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 6862422
zbMATH Keywords: representations of \(\mathrm{SO}(3)\) and \(\mathrm{SU}(2)\)
zbMATH Keywords: Clebsch-Gordan coefficient
zbMATH Keywords: harmonic polynomial
MaRDI profile type: Publication
cites work: Q3996834
cites work: Q4895354
cites work: Q4535231
cites work: Q4824155
full work available at URL: s0037446617060088
OpenAlex ID: W2790451801
description: scientific article; zbMATH DE number 6862422