Title

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

Department/School

Mathematics

Date

1-1-2017

Document Type

Paper

Abstract

Patrias and Pylyavskyy introduced shifted Hecke insertion as an application of their theory of dual filtered graphs. We study shifted Hecke insertion, showing it preserves descent sets and relating it the K-theoretic jeu de taquin of Buch–Samuel and Clifford–Thomas–Yong. As a consequence, we construct symmetric functions that are closely related to Ikeda–Naruse's representatives for the K-theory of the orthogonal Grassmannian. Exploiting this relationship and introducing a shifted K-theoretic Poirier–Reutenauer algebra, we derive a Littlewood–Richardson rule for the K-theory of the orthogonal Grassmannian equivalent to the rules of Clifford–Thomas–Yong and Buch–Samuel.

Published in

Proceedings of the 29th Conference on Formal Power Series and Algebraic Combinatorics

Citation/Other Information

Hamaker, Z., Keilthy, A., Patrias, R., Webster, L., Zhang, Y., & Zhou, S. (2017). Shifted hecke insertion and the k-theory of OG(n, 2n + 1). Séminaire Lotharingien de Combinatoire 78B, Proceedings of the 29th Conference on Formal Power Series and Algebraic Combinatorics, no. 14.

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