PDF Page 446 http://www.itp.phys.ethz.ch/research/qftstrings/archive/13HSStrings/StringsHS13Notes.pdf
"$[J_3,J^+] = J_3, [J_3,J^{-}] = - J_3$, In intuitive terms, this tells us the charges of $J^{\pm}$ with respect to the $U(1)$ subgroup generated by the Cartan $J_3$."
Huh?