论文标题
通过冰的舒伯特多项式的Gröbner几何形状
Gröbner geometry of Schubert polynomials through ice
论文作者
论文摘要
Knutson和Miller（2005）通过Matrix Schubert品种的AntiagonalGröbner变性建立了Schubert多项式及其组合梦想形式的几何自然性。我们认为对角线Gröbner变性。在这种双重环境中，诺特森，米勒和杨（2009）获得了“ vexillary'Matrix schubert品种类别的替代组合，我们启动了一般对角线变性的研究，将它们与lascoux（2002年的被忽视的LASCOUX（2002年）的否决（以6 $ -RAM-vertex Ice的模型）相关联（2002年），并将其与shyme（$ -RAM）相关联（2002年）。 （2018年）以“浮力斗篷梦”为幌子。
The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this dual setting, Knutson, Miller, and Yong (2009) obtained alternative combinatorics for the class of "vexillary'' matrix Schubert varieties. We initiate a study of general diagonal degenerations, relating them to a neglected formula of Lascoux (2002) in terms of the $6$-vertex ice model (recently rediscovered by Lam, Lee, and Shimozono (2018) in the guise of "bumpless pipe dreams'').
