please read page 77 of the pdf at the link...the full proof is laid out... the theorem is clear and I don't see mistakes yet that passage to prove the lemma is obscure. Wikipedia refers to that book...https://en.wikipedia.org/wiki/Representation_theory_of_SU%282%29 ...
"Weights and the structure...
Hi all I need to understand the following passage from Hall link page 78 :
Some notation first:
Basis for ##sl(2;C)##:
##H=\begin{pmatrix} 1&0\\0&−1\end{pmatrix} ;X=\begin{pmatrix} 0&1\\0&0\end{pmatrix} ;Y=\begin{pmatrix} 0&0\\1&0\end{pmatrix} ##
which have the commutation relations...