  We explicitly constructed the generators of $SU(n+1)$ group which commute
with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the
background U(n) gauge fields. The corresponding Hamiltonian can be represented
as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$
group contains our bosonic and fermionic coordinates and momenta, while the
second one, on the SU(1,n) group, is constructed from isospin degrees of
freedom only.
