论文标题
关于考奇公式的注释
A note on Cauchy's formula
论文作者
论文摘要
我们使用顶点操作员的相关函数来给出Cauchy的公式\ begin {align*} \ prod^k_ {i = 1} \ prod^n_ {j = 1}（1-x_iy_j）= \ sum_ n]}（-1）^{|μ|}s_μ\ {x \} s_ {μ'} \ {y \}。 \ end {align*}作为解释的应用，我们在半平面分区中获得了$ \ prod^\ infty_ {i = 1}（1-q^i）^{i-1} $的扩展。
We use the correlation functions of vertex operators to give a proof of Cauchy's formula \begin{align*} \prod^K_{i=1}\prod^N_{j=1}(1-x_iy_j)=\sum_{μ\subseteq [K\times N]}(-1)^{|μ|}s_μ\{x\}s_{μ'}\{y\}. \end{align*} As an application of the interpretation, we obtain an expansion of $\prod^\infty_{i=1}(1-q^i)^{i-1}$ in terms of half plane partitions.
