## Lee, Seung Jin - Pieri rule for the affine flag variety

dmtcs:2517 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Pieri rule for the affine flag variety

Authors: Lee, Seung Jin

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.

Source : oai:HAL:hal-01337837v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: affine flag variety,$k$ -Schur function,nilCoxeter algebra,Pieri rule,strong Schur function,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]