  $Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric
matrix coordinates are classified. Analogous results are obtained for
Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski
space as a particular case. The constructed equations are associated with the
tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank
${\mathbf{r }}$. The infinite set of higher-spin conserved currents multilinear
in rank-one fields in ${\cal M}_M$ is found. The associated conserved charges
are supported by $({\mathbf{r }} M-\frac{{\mathbf{r }} ({\mathbf{r }}
-1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by
virtue of the rank-$2{\mathbf{r }}$ field equations. The cohomology groups
$H^p(\sigma^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine
the form of appropriate gauge fields and their field equations, are found both
for ${\cal M}_M$ and for its Minkowski-like subspace.
