Geodesic
Pieri rule for the affine flag variety
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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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. 
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     author = {Lee, Seung Jin},
     title = {Pieri rule for the affine flag variety},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2517},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2517/}
}
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Lee, Seung Jin. Pieri rule for the affine flag variety. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2517. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2517/

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