Symmetric spaces and Higgs models in the method of dimensional reduction. II. Theories with one multiplet of scalar fields

In the present paper which is the continuation of [1] we study the gauge models obtained by means of the dimensional reduction of pure multidimensional gauge theories with symmetries. We investigate properties of a class of subalgebras of the classical Lie algebras (which includes both regular and non-regular subalgebras) and find a sufficient condition for the reduced theory to contain only one irreducible multiplet of scalar fields. Some examples of the explicit construction of such theories are given in the case where the space of extra dimensions is the sphere $S^l$.