论文标题
转移的双重稳定Grothendieck多项式的组合公式
Combinatorial formulas for shifted dual stable Grothendieck polynomials
论文作者
论文摘要
$ k $ - 理论schur $ p $ - 和$ q $ - functions $gp_λ$和$gq_λ$可以具体地定义为SemistArdard Shifted Set-Set-Set-set-valued tableaux的重量生成功能。这些对称函数是稳定的Grothendieck多项式的移位类似物，由Ikeda和Naruse引入几何形状。 Nakagawa和Naruse指定的双$ k $ - 理论schur $ p $ - 和$ q $ functions $gp_λ$和$gq_λ$通过涉及$gp_λ$和$gq_λ$的$gp_λ$和$gq_λ$。他们猜想双功率系列是某些移位平面分区的重量生成功能。我们证明了这个猜想。我们还为$gp_λ$和$gq_λ$的图像中的$ω$相关函数的相关函数提供了一个相关的生成函数公式。这证实了Chiu和第二作者的猜想。使用这些结果，我们验证了ikeda和Naruse的猜想，即$ gq $ - 功能是环的基础。
The $K$-theoretic Schur $P$- and $Q$-functions $GP_λ$ and $GQ_λ$ may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmetric functions are the shifted analogues of stable Grothendieck polynomials, and were introduced by Ikeda and Naruse for applications in geometry. Nakagawa and Naruse specified families of dual $K$-theoretic Schur $P$- and $Q$-functions $gp_λ$ and $gq_λ$ via a Cauchy identity involving $GP_λ$ and $GQ_λ$. They conjectured that the dual power series are weight generating functions for certain shifted plane partitions. We prove this conjecture. We also derive a related generating function formula for the images of $gp_λ$ and $gq_λ$ under the $ω$ involution of the ring of symmetric functions. This confirms a conjecture of Chiu and the second author. Using these results, we verify a conjecture of Ikeda and Naruse that the $GQ$-functions are a basis for a ring.
