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

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.

preprint2015arXivOpen access
Zachary HamakerAdam KeilthyRebecca PatriasLillian WebsterYinuo ZhangShuqi Zhou
math.CO
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Zachary HamakerAdam KeilthyRebecca PatriasLillian WebsterYinuo ZhangShuqi Zhou

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