Consider a Clebsch-Gordan expansion $R\_i\bigotimes{R\_j}=\bigoplus\_p{R\_p}$. Assume the irrep $R\_k$ does NOT appear in the sum on the right side. Does it now follow that the "triangle" ${R\_i,R\_j,R\_k}$ is "inaccessible" and consequently the 6j symbol
$
\begin{Bmatrix}
R\_i & R\_j & R\_k\\\
R\_l & R\_m & R\_n
\end{Bmatrix}
$
vanishes for any entries ${R\_l,R\_m,R\_n}$ ?


(And what about a converse? After all, 6j symbols have accidental zeroes. But can ALL 6j symbols with some fixed upper row accidentally vanish even if the upper row forms an accessible triangle?)



Simple 6j symbol question
Doc, not sure what "inaccessible" but the second question is a tautology. Your $6j$ symbol is a linear map $\hom(R\_k,R\_i\otimes R\_j)\otimes\hom(R\_m,R\_k\otimes R\_l)\rightarrow \hom(R\_n,R\_j\otimes R\_l)\otimes \hom(R\_m,R\_i\otimes R\_n)$. It is zero because the left vector space is zero.


