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

Relating the type A alcove path model to the right key of a semistandard Young tableau, with Demazure character consequences