Representations · workbench

Tensor products

Decompose two SU(2) representations with exact multiplicities.

Supported: SU(2), highest weights 0–30

Exact decomposition2 summands

V_{1}\otimes V_{1}=V_{0}\oplus V_{2}

$V_n$ has highest weight $n$ , spin $n/2$ and complex dimension $n+1$ . Every summand here occurs once.

SU(2) tensor product summands
Highest weight	Spin j	Dimension	Multiplicity
0	$0$	1	1
2	$1$	3	1

Method, conventions & sources

SU(2) Clebsch–Gordan rule, highest weights |a-b| through a+b in increments of 2.

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