格图行列式的消失理想
Vanishing ideals of Lattice Diagram determinants
摘要：
晶格图是正象限中晶格单元的有限集合$L=\{(p_1,q_1),... ,(p_n,q_n)\}$。相应的点阵图行列式是$Δ_L(\X;\Y)=\det \| x_i^{p_j}y_i^{q_j} \|$。空间$M_L$是由$Δ_L(\X;\Y)$的所有偏导数所张成的空间。我们用$M_L^0$表示$M_L$的无$Y$组分.对于$n+1$的一个划分，我们用$μ/ij$表示从$μ$的费勒斯图中去掉单元格$(i,j)$所得到的图。利用齐次部分对称多项式，给出了$M_μ^0$空间的消失理想的对偶描述，并首次给出了$M_{μ/ij}^0$的消失理想的描述.
英文摘要：
A lattice diagram is a finite set $L=\{(p_1,q_1),... ,(p_n,q_n)\}$ of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is $Δ_L(\X;\Y)=\det \| x_i^{p_j}y_i^{q_j} \|$. The space $M_L$ is the space spanned by all partial derivatives of $Δ_L(\X;\Y)$. We denote by $M_L^0$ the $Y$-free component of $M_L$. For $μ$ a partition of $n+1$, we denote by $μ/ij$ the diagram obtained by removing the cell $(i,j)$ from the Ferrers diagram of $μ$. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the space $M_μ^0$ and we give the first known description of the vanishing ideal of $M_{μ/ij}^0$.
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