论文标题
双Grothendieck多项式和彩色晶格模型
Double Grothendieck polynomials and colored lattice models
论文作者
论文摘要
我们构建了一个可集成的彩色六个vertex模型，其分区函数是双重粒度多项式。这提供了对富裕的管道梦的可集成系统解释，以及Weigandt [arxiv：2003.07342]的最新结果，将双Grothendieck多个月素与浮力的Pipe Dreams联系起来。对于Vexillary排列，我们构建了一个新的模型，我们称为半单词版本模型。我们使用Motegi和sakai的半传说模型和五个vertex模型给出了一个新的证据，即双侧面置换式置换术的双重置换术都等于标记的阶段性粒度Grothendieck多项式。采用双重粒度多项式的稳定限制，我们获得了一个新的证据，即稳定的极限是麦克纳马拉定义的阶乘Grothendieck多项式。我们的半学模型的状态自然对应于非电向晶格路径的家族，然后我们可以使用lindström-gessel-viennot引理为对应于Vexillary Permudations的双重舒伯特多项式提供了决定性公式。
We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe dreams and recent results of Weigandt [arXiv:2003.07342] relating double Grothendieck polynomias with bumpless pipe dreams. For vexillary permutations, we then construct a new model that we call the semidual version model. We use our semidual model and the five-vertex model of Motegi and Sakai to given a new proof that double Grothendieck polynomials for vexillary permutations are equal to flagged factorial Grothendieck polynomials. Taking the stable limit of double Grothendieck polynomials, we obtain a new proof that the stable limit is a factorial Grothendieck polynomial as defined by McNamara. The states of our semidual model naturally correspond to families of nonintersecting lattice paths, where we can then use the Lindström-Gessel-Viennot lemma to give a determinant formula for double Schubert polynomials corresponding to vexillary permutations.
