论文标题
精制的双重色态多项式，集成性和Schur度量
Refined dual Grothendieck polynomials, integrability, and the Schur measure
论文作者
论文摘要
我们构建了一个顶点模型，其分区函数是一种精制的双重粒度多项式，其中状态被解释为非电向晶格路径。使用此过程，我们显示了精制的双重色迪多项式是多功能函数，并具有许多身份，包括Littlewood和Cauchy（-little Wood）身份。然后，我们完善了Yeliussizov在双重性多项式和Johansson讨论的最后一段渗透过程（LPP）随机过程之间的联系。通过完善约翰逊的代数技术，我们展示了Grinberg猜想的偏向于精制的双重Grothendieck多项式的Jacobi-Trudi公式，并恢复了由于Baik和Rains引起的LPP与Schur过程之间的关系。最后，我们扩展了顶点模型技术，以显示一些精致的Grothendieck多项式（包括Jacobi-Trudi公式）的身份。
We construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we show refined dual Grothendieck polynomials are multi-Schur functions and give a number of identities, including a Littlewood and Cauchy(-Littlewood) identity. We then refine Yeliussizov's connection between dual Grothendieck polynomials and the last passage percolation (LPP) stochastic process discussed by Johansson. By refining algebraic techniques of Johansson, we show Jacobi-Trudi formulas for skew refined dual Grothendieck polynomials conjectured by Grinberg and recover a relation between LPP and the Schur process due to Baik and Rains. Lastly, we extend our vertex model techniques to show some identities for refined Grothendieck polynomials, including a Jacobi-Trudi formula.
