Pieri rule for the affine flag variety

2014/06/17 by Seung Jin Lee, Lee, Seung Jin · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1406.4246

14 pages, Fixed typos

arxiv created 2015/04/15 · arxiv updated 2015/04/16

Abstract

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.

Cited by

• Simple modules for affine nilCoxeter algebras
• The combinatorial geometry of particle physics

Related

• Equivariant Pieri Rule for the homology of the affine Grassmannian
• A Pieri-type Formula for the Equivariant Cohomology of the Flag Manifold
• Some questions arising from the study of cohomology on flag varieties
• Pieri operators on the affine nilCoxeter algebra
• The Leray-Hirsch Theorem for equivariant oriented cohomology of flag varieties