论文标题
浮力的梦想和交替的标志矩阵
Bumpless pipe dreams and alternating sign matrices
论文作者
论文摘要
在他们在无限旗品种上的工作中，林，李和Shimozono（2018）引入了称为Bumpless Pipe Dreams的对象，并用它们为双舒伯特多项式提供了公式。我们将此公式扩展到K理论的设置，从而使双Grothendieck多项式的表达方式是对较大类别的富有浮力的Pipe Dreams的总和。我们的证明取决于Lascoux（2002）未出版的手稿中发现的技术。 Lascoux展示了如何在交替的符号矩阵上写双Grothendieck多项式。我们解释了如何将Lam-Lee-Shimozono公式视为Lascoux交替符号矩阵公式的伪装的特殊情况。 Knutson，Miller和Yong（2009）给出了一个弱Grothendieck多项式的图表。我们通过展示疲惫不堪的笨拙的烟斗梦和标记的设定值tableaux来恢复此公式，以保留重量。最后，我们在Hecke Bumpless Pipe Dreams和减少Tableaux之间进行了两者的培训。对Edelman-Greene Bumpless Pipe Dreams的两次培养的限制解决了Lam，Lee和Shimozono的问题。
In their work on the infinite flag variety, Lam, Lee, and Shimozono (2018) introduced objects called bumpless pipe dreams and used them to give a formula for double Schubert polynomials. We extend this formula to the setting of K-theory, giving an expression for double Grothendieck polynomials as a sum over a larger class of bumpless pipe dreams. Our proof relies on techniques found in an unpublished manuscript of Lascoux (2002). Lascoux showed how to write double Grothendieck polynomials as a sum over alternating sign matrices. We explain how to view the Lam-Lee-Shimozono formula as a disguised special case of Lascoux's alternating sign matrix formula. Knutson, Miller, and Yong (2009) gave a tableau formula for vexillary Grothendieck polynomials. We recover this formula by showing vexillary marked bumpless pipe dreams and flagged set-valued tableaux are in weight preserving bijection. Finally, we give a bijection between Hecke bumpless pipe dreams and decreasing tableaux. The restriction of this bijection to Edelman-Greene bumpless pipe dreams solves a problem of Lam, Lee, and Shimozono.
