Schubert graphs,symmetric groups and flags of Boolean lattices

We introduce the concept of Schubert graphs, as Schubert spaces — in the meaning of A. Bichara and C. Somma 2] — whose lines have exactly two points. They turn out to be isomorphic to particular Cayley graphs of symmetric groups; this leads also to a new proof of a well-known characterization of symmetric groups. In connection with 2], we prove that a Schubert graph is isomorphic to the graph representing the flags of a Boolean lattice. Finally, we discuss the independence of the axioms.To Professor Adriano Barlotti on the occasion of his seventieth birthday