论文标题
可集成的型号和$ k $ - Grothendieck课程的理论推送
Integrable models and $K$-theoretic pushforward of Grothendieck classes
论文作者
论文摘要
我们表明，由Shigechi和Uchiyama得出的可集成晶格模型的Yang-Baxter代数的多个换向关系可用于连接两种类型的Grothendieck类，由$ k $ - 理论推送 - 从Grothendieck的Grothendieck小组的Grothendieck小组与Grethendieck Grout to Grothendieck组相连。 Using the commutation relation, we show that two types of partition functions of an integrable five-vertex model, which can be explicitly described using skew Grothendieck polynomials, and can be viewed as Grothendieck classes, are directly connected by the $K$-theoretic pushforward.我们表明，与Nonskew版本相对应的Pushforward公式的特殊情况也是Buch得出的公式的特殊情况。我们还提出了Guo和Sun对Grothendieck多项式的身份的偏斜概括，这是Fehér，Némethi和Rimányi的Schur多项式术的延伸。我们还显示了推送公式的应用，并得出了Grothendieck多项式的集成公式。
We show that a multiple commutation relation of the Yang-Baxter algebra of integrable lattice models derived by Shigechi and Uchiyama can be used to connect two types of Grothendieck classes by the $K$-theoretic pushforward from the Grothendieck group of Grassmann bundles to the Grothendieck group of a nonsingular variety. Using the commutation relation, we show that two types of partition functions of an integrable five-vertex model, which can be explicitly described using skew Grothendieck polynomials, and can be viewed as Grothendieck classes, are directly connected by the $K$-theoretic pushforward. We show that special cases of the pushforward formula which correspond to the nonskew version are also special cases of the formulas derived by Buch. We also present a skew generalization of an identity for the Grothendieck polynomials by Guo and Sun, which is an extension of the one for Schur polynomials by Fehér, Némethi and Rimányi. We also show an application of the pushforward formula and derive an integration formula for the Grothendieck polynomials.
