RATIONAL CLASSIFICATION OF SIMPLE FUNCTION-SPACE COMPONENTS FOR FLAG MANIFOLDS

Let M(X, Y) denote the space of all continuous functions between X and Y and M-f(X, Y) the path component corresponding to a given map f:X - -> Y. When X and Y are classical flag manifolds, we prove the componen ts of M(X, Y) corresponding to ''simple'' maps f are classified up to rational homotopy type by the dimension of the kernel off in degree tw o cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.