Demazure crystals for Kohnert polynomials

Kohnert polynomials are indexed by unit cell diagrams in the first quadrant defined earlier author and Searles that give a common generalization of Schubert Demazure characters for general linear group. crystals certain truncations normal whose characters. For each diagram satisfying southwest condition, we construct crystal character is polynomial given diagram, resolving an conjecture these expand nonnegatively into We explicit formulas expansions with applications including characterization those which corresponding single character.