  We study quantum Hall ferromagnets with a finite density topologically
charged spin textures in the presence of internal degrees of freedom such as
spin, valley, or layer indices, so that the system is parametrised by a
$d$-component complex spinor field. In the absence of anisotropies, we find
formation of a hexagonal Skyrmion lattice which completely breaks the
underlying SU(d) symmetry. The ground state charge density modulation, which
inevitably exists in these lattices, vanishes exponentially in $d$. We compute
analytically the complete low-lying excitation spectrum, which separates into
$d^{2}-1$ gapless acoustic magnetic modes and a magnetophonon. We discuss the
role of effective mass anisotropy for SU(3)-valley Skyrmions relevant for
experiments with AlAs quantum wells. Here, we find a transition, which breaks a
six-fold rotational symmetry of a triangular lattice, followed by a formation
of a square lattice at large values of anisotropy strength.
