  Stanley symmetric functions are the stable limits of Schubert polynomials. In
this paper, we show that, conversely, Schubert polynomials are Demazure
truncations of Stanley symmetric functions. This parallels the relationship
between Schur functions and Demazure characters for the general linear group.
We establish this connection by imposing a Demazure crystal structure on key
tableaux, recently introduced by the first author in connection with Demazure
characters and Schubert polynomials, and linking this to the type A crystal
structure on reduced word factorizations, recently introduced by Morse and the
second author in connection with Stanley symmetric functions.
