  The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5
sigma model as well as a limit of a nonlinear topological A-model, introduced
by Berkovits. We study the latter, especially its symmetries, and map them to
higher spin algebras.
  We show the following. The linear A-model possesses affine
$\AKMSA{pgl}{4}{4}_0$ symmetry at critical level and its $\AKMSA{psl}{4}{4}_0$
current-current perturbation is the nonlinear model. We find that the
perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical
level. There is a topological algebra associated to $\AKMSA{pgl}{4}{4}_0$ with
the properties that the perturbation is BRST-exact. Further, the
BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the
non-trivial generators of the $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor
maps the linear model to a higher spin theory. We analyze its
$\SLSA{psl}{4}{4}$ action and find finite dimensional short multiplets.
