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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*,2*n*+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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