Buch and Rimanyi proved a formula for specializations of double Grothendieck polynomials based on the Yang-Baxter equation related to the degenerate Hecke algebra. A geometric proof was found by Yong and Woo by constructing a Grobner basis for the Kazhdan-Lusztig ideals. In this note, we give an elementary proof for this formula by using only divided difference operators.

中文翻译：

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关于 Grothendieck 多项式的特化的注释

Buch 和 Rimanyi 基于与退化 Hecke 代数相关的 Yang-Baxter 方程，证明了双格洛腾迪克多项式的特化公式。Yong 和 Woo 通过为 Kazhdan-Lusztig 理想构建 Grobner 基础找到了几何证明。在本笔记中，我们仅使用除差算子给出了该公式的基本证明。