Séminaire Lotharingien de Combinatoire, 78B.14 (2017), 12 pp.

Zachary Hamaker, Adam Keilthy, Rebecca Patrias, Lillian Webster, Yinuo Zhang and Shuqi Zhou

Shifted Hecke insertion and K-theory of OG(n,2n+1)

Abstract. Patrias and Pylyavskyy introduced shifted Hecke insertion as an application of their theory of dual filtered graphs. We show that shifted Hecke insertion has a natural place in the combinatorial study of the K-theory of the maximal orthogonal Grassmannian. In particular, we relate it to the K-theoretic jeu de taquin of Clifford-Thomas-Yong and use it to create new symmetric functions, which we use to derive a Littlewood-Richardson rule for the K-theory of the orthogonal Grassmannian equivalent to the rules of Clifford-Thomas-Yong and Buch-Samuel.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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