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arXiv · 1510.08972

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

Zachary Hamaker·Adam Keilthy·Rebecca Patrias·Lillian Webster·Yinuo Zhang·Shuqi Zhou
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Abstract

Patrias and Pylyavskyy introduced shifted Hecke insertion as an application of their theory of dual filtered graphs. We use shifted Hecke insertion to construct symmetric function representatives for the K-theory of the orthogonal Grassmannian. These representatives are closely related to the shifted Grothendieck polynomials of Ikeda and Naruse. We then recover the K-theory structure coefficients of Clifford-Thomas-Yong/Buch-Samuel by introducing a shifted K-theoretic Poirier-Reutenauer algebra. Our proofs depend on the theory of shifted K-theoretic jeu de taquin and the weak K-Knuth relations.

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Zachary Hamaker, Adam Keilthy, Rebecca Patrias, Lillian Webster, Yinuo Zhang, Shuqi Zhou. 2015-10-30. Shifted Hecke insertion and the K-theory of OG(n,2n+1). https://arxiv.org/abs/1510.08972

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