Timeline for Clebsch–Gordan decomposition for $\mathrm{SU}(2)$, in indices

4 events

when toggle format	what		by	license	comment
Aug 15, 2018 at 15:00	vote	accept	onamoonlessnight
Aug 14, 2018 at 14:04	comment	added	Abdelmalek Abdesselam		No there are not. The physicist's CG coefficients $\langle j_1 m_1 j_2 m_2\|j_3 m_3\rangle$ are matrix elements of explicit projectors (or injections given by the transpose) of $\pi_{\mu}\otimes\pi_{\nu}$ onto some irreducible $\pi_{\lambda}$. The mathematician's CG coefficient $c(\mu,\nu;\lambda)$ is the multiplicity of the irreducible in the tensor product.
Aug 12, 2018 at 10:36	comment	added	onamoonlessnight		It took me a while to parse the notation but this seems to be what I wanted. Are the Clebsch--Gordan coefficients $\langle j_1 m_1 j_2 m_2 \| j_3 m_3 \rangle $ there the same as the ones one would call the CG coefficients $c(\mu, \nu; \lambda)$ in the expansion $ \pi_\mu \otimes \pi_\nu = \bigoplus_\lambda c(\mu, \nu; \lambda) \pi_\lambda$, in that I would have $c = 0$ or $1$ for $\mathrm{SU}(2)$?
Aug 10, 2018 at 14:54	history	answered	Abdelmalek Abdesselam	CC BY-SA 4.0