A symplectic refinement of shifted Hecke insertion

摘要

Buch, Kresch, Shimozono, Tamvakis, and Yong defined Hecke insertion to formulate a combinatorial rule for the expansion of the stable Grothendieck polynomials G(pi) indexed by permutations in the basis of stable Grothendieck polynomials G(lambda) indexed by partitions. Patrias and Pylyavskyy introduced a shifted analogue of Hecke insertion whose natural domain is the set of maximal chains in a weak order on orbit closures of the orthogonal group acting on the complete flag variety. We construct a generalization of shifted Hecke insertion for maximal chains in an analogous weak order on orbit closures of the symplectic group. As an application, we identify a combinatorial rule for the expansion of "orthogonal" and "symplectic" shifted analogues of G(pi) in Ikeda and Naruse's basis of K-theoretic Schur P-functions. (c) 2020 Elsevier Inc. All rights reserved.