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.

Buch，Kresch，Shimozono，Tamvakis和Yong定义了Hecke插入，从而为稳定的Grothendieck多项式的展开制定了组合规则 $G_{\pi }$ 在稳定的Grothendieck多项式的基础上通过置换索引 $G_{\lambda }$由分区索引。Patrias和Pylyavskyy引入了Hecke插入的移位类似物，其自然域是作用在完整标志变体上的正交群的轨道闭合上的弱链最大链组。我们在辛群的轨道闭合上以相似的弱顺序构造了最大链移位Hecke插入的一般化。作为一种应用，我们确定了扩展的“正交”和“折衷”移位类似物的组合规则$G_{\pi }$在池田和成濑的K理论Schur P函数的基础上。