In this paper, we first calculate the orthogonal basis of the vector space spanned by e_ie_je_ke₀|0⟩, where e_j are the generators of the affine Yangian of $\mathfrak{g}\mathfrak{l}(1)$. The elements of this orthogonal basis correspond to three dimensional bosons. Then, we calculate the Schur functions of plane partitions of 4, we find that the plane partitions become Young diagrams, and the Schur functions on plane partitions become Schur functions on Young diagrams when h₁ = 1, h₂ = −1, and h₃ = 0.

中文翻译：

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4 平面分区上的仿射 Yangian 和 Schur 函数

在本文中，我们首先计算由e _i e _j e _k e ₀ |0⟩跨越的向量空间的正交基，其中e _j是$\mathfrak{G}\mathfrak{升}(1)$. 这个正交基的元素对应于三维玻色子。然后，我们计算4的平面分区的Schur函数，我们发现当h ₁ = 1、h ₂ = -1、h时，平面分区成为Young图，平面分区上的Schur函数成为Young图上的Schur函数₃ = 0。