We prove the affine Pieri rule for the cohomology of the affine flag variety
conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on
the affine nilHecke ring that is motivated by Kostant and Kumar's work on the
equivariant cohomology of the affine flag variety. We show that the cap
operators for Pieri elements are the same as Pieri operators defined by Berg,
Saliola and Serrano. This establishes the affine Pieri rule.Comment: 14 pages, Fixed typo