  Flagged Schur modules generalize the irreducible representations of the
general linear group under the action of the Borel subalgebra. Their characters
include many important generalizations of Schur polynomials, such as Demazure
characters, flagged skew Schur polynomials, and Schubert polynomials. In this
paper, we prove the characters of flagged Schur modules can be computed using a
simple combinatorial algorithm due to Kohnert if and only if the indexing
diagram is northwest. This gives a new proof that characters of flagged Schur
modules are nonnegative sums of Demazure characters and gives a representation
theoretic interpretation for Kohnert polynomials.
