  A mapping between operators on the Hilbert space of $N$-dimensional quantum
system and the Wigner quasiprobability distributions defined on the symplectic
flag manifold is discussed. The Wigner quasiprobability distribution is
constructed as a dual pairing between the density matrix and the
Stratonovich-Weyl kernel. It is shown that the moduli space of the
Stratonovich-Weyl kernel is given by an intersection of the coadjoint orbit
space of the $SU(N)$ group and a unit $(N-2)$-dimensional sphere. The general
consideration is exemplified by a detailed description of the moduli space of
2, 3 and 4-dimensional systems.
