  We construct the representations of general dimension for the soliton
solution to the $SU(2)$ Skyrme model, and show that at the classical level the
dependence on the dimension of the representation ($2j+1$) appears only as an
overall factor $j(j+1)(2j+1)$ in the Lagrangian density, which may be absorbed
by a rescaling of the parameters. Alternate stabilizing terms in the model will
in general have a different $j$-dependence and have to be rescaled accordingly
in order to achieve representation independent predictions. In contrast the
quantum corrections do depend on the dimension of the representation and in
general differ from those obtained in the fundamental representation of
$SU(2)$.
