As we know, the Projective space P^n represent the functor sending X to the set of line bundles L on X together with a surjection from the trivial vector bundle to L.

My question is, what functor does the grassmannian Gr(d,n) represent? Sending X to the set of rank n vector bundles together with a subbundle of rank d?

More generally, what functor does flag varieties represent?