Maps · workbench

Branching & embeddings

Follow the regular or principal map into SU(3).

Supported: SU(3) fundamental and adjoint

Selected SU(3) restrictionImage SU(2)

\left.\mathbf{8}\right|_{\mathrm{SU}(2),\,\mathrm{regular}}=\mathbf{3}\oplus \mathbf{2}\oplus \mathbf{2}\oplus \mathbf{1}

Domain of group map: $\mathrm{SU}(2)$
Image subgroup: $\mathrm{SU}(2)$
Kernel of group map: $\{1\}$

The regular group embedding is $A\mapsto\operatorname{diag}(A,1)$ . It is injective, and its image is an SU(2) subgroup. Output numbers denote complex dimensions.

Branching multiplicities
Output dimension	Spin j	Multiplicity
3	$1$	1
2	$\frac{1}2$	2
1	$0$	1

Dimension check: $3 + 2 + 2 + 1 = 8$ . The calculation retains every repeated summand. Supported parent representations: 3 and 8.

Method, conventions & sources

Curated restrictions of SU(3) representations 3 and 8 along the regular and principal maps; repeated summands are retained.

Finite-dimensional complex representations; Hermitian generators; tr_fund(T^a T^b) = delta_ab/2; T(R) dim(g) = C2(R) dim(R).

Calculation version: groups-design-1.0.0

How calculation links, versions, and exports work