On affine Toda field theories related to D_r algebras and their real Hamiltonian forms

The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series D-r. We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of g. This is illustrated on the examples D-r+1((1)) -> B-r((1)) and D-4((1)) -> G(2)((1)) using external automorphisms of the corresponding extended Dynkin diagrams.