  There are several combinatorial methods that can be used to produce type A
Demazure characters (key polynomials). The alcove path model of Lenart and
Postnikov provides a procedure that inputs a semistandard tableau $T$ and
outputs a saturated chain in the Bruhat order. The final permutation in this
chain determines a family of Demazure characters for which $T$ contributes its
weight. Separately, the right key of $T$ introduced by Lascoux and
Sch\"utzenberger also determines a family of Demazure characters for which $T$
contributes its weight. In this paper we show that the final permutation in the
chain produced by the alcove model corresponds bijectively to the right key of
the tableau. From this it follows that the generating sets for the Demazure
characters produced by these two methods are equivalent.
