Unitary symmetry and dynamics of high-spin magnets in Weyl and Racah bases

We have studied the dynamics of none-quilibrium states of high-spin magnets (s>1/2) in a Weyl and Racah basis. We have established non-linear equations of the dynamics of magnets with arbitrary spin and studied the case of the spin s=1;3/2 in detail. We have found expressions for Casimir invariants in case of pure quantum states and established inequalities that characterize magnetic degrees of freedom for mixed quantum states. We have calculated the explicit form of the polarization density matrix for pure quantum states of magnets with spins s=1 and s=3/2.