On topological excitations with isovector topological charges

It is shown that degenerate systems with order parameter ψ taking on values in compact homogeneous subspaces T _G or G/T _G (where G is a simple compact group and T _G is its maximum commutative subgroup) possess a rich collection of topological excitations (vortices or, correspondingly, instantons) with isovector topological charges. The corresponding homotopy groups are found for all G. The possibility of a topological interpretation of the quantum numbers of the groups and particles is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 758–762 (25 May 1996)