The well-separated ground state of the 4-fold degeneracy (Gamma(8) qua
rtet) of a Ce3+ ion is an important prerequisite of the quadrupolar or
dering in CeB6. A new description for the Gamma(8) quartet is proposed
in terms of spin-like and orbital-like Pauli matrices, sigma and tau.
A unusual dependence of orbital ordering on magnetic field H and temp
erature T is explained in terms of mode-coupling effects. The theory n
aturally explains the orbitally modulated [1/21/21/2] structure, the t
ransition temperature behaviour, T-Q vs H, as well as the growing anom
aly of the specific heat at T-Q(H) with H increasing. Similar approach
in terms of sigma and tau matrices is available for the one f-hole co
mpounds, e.g., TmTe.