Sp(2M) invariant field equations in the space MMβ with symmetric
matrix coordinates are classified. Analogous results are obtained for
Minkowski-like subspaces of MMβ 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
r. The infinite set of higher-spin conserved currents multilinear
in rank-one fields in MMβ is found. The associated conserved charges
are supported by (rMβ2r(rβ1)β)βdimensional differential forms in MMβ, that are closed by
virtue of the rank-2r field equations. The cohomology groups
Hp(Οβrβ) with all p and r, which determine
the form of appropriate gauge fields and their field equations, are found both
for MMβ and for its Minkowski-like subspace.Comment: 27 pages; V2: Significant extension of the results to computation of
all Οββ cohomologies, 43 pages; V3: Discussion of equations in
generalized Minkowski space from the perspective of usual Minkowski space and
reference added, typos corrected, the journal version, 44 page