Pieri rule for the affine flag variety

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• 作者：Seung Jin Lee ^{lsjin@kias.re.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Affine flag variety ; k-Schur function ; NilCoxeter algebra ; Pieri rule ; Strong Schur function
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：266-284
• 全文大小：398 K

文摘

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. We also discuss properties of cap operators which are not necessarily affine A type.