  We consider the Dirac equation with an external Yang-Mills gauge field in a
homogeneous space with an invariant metric. The Yang-Mills fields for which the
motion group of the space serves as the symmetry group for the Dirac equation
are found by comparison of the Dirac equation with an invariant matrix
differential operator of the first order. General constructions are illustrated
by the example of de Sitter space. The eigenfunctions and the corresponding
eigenvalues for the Dirac equation are obtained in the space
$\mathbb{R}^2\times \mathbb{S}^2$ by a noncommutative integration method.
