  Large $N$ but non-planar limits of ${\cal N}=4$ super Yang-Mills theory can
be described using restricted Schur polynomials. Previous investigations
demonstrate that the action of the one loop dilatation operator on restricted
Schur operators, with classical dimension of order $N$ and belonging to the
$su(2)$ sector, is largely determined by the $su(2)$ ${\cal R}$ symmetry
algebra as well as structural features of perturbative field theory. Studies
presented so far have used the form of ${\cal R}$ symmetry generators when
acting on small perturbations of half-BPS operators. In this article, as a
first step towards going beyond small perturbations of the half-BPS operators,
we explain how the exact action of symmetry generators on restricted Schur
polynomials can be determined.
