  It is shown how one can define vector topological charges for topological
exitations of non-linear sigma-models on compact homogeneous spaces T_G and
G/T_G (where G is a simple compact Lie group and T_G is its maximal commutative
subgroup). Explicit solutions for some cases, their energies and interaction of
different topological charges are found. A possibility of the topological
interpretation of the quantum numbers of groups and particles is discussed.
