Local cohomology with support in ideals of symmetric minors and Pfaffians
Local cohomology with support in ideals of symmetric minors and Pfaffians
复制标题
支持对称次要和普法夫理想的局部上同调
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Weyman
中科院分区：
文献类型：
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作者：
Claudiu Raicu;J. Weyman
对于一般线性群GL在X上的自然作用，我们计算了局部上同调模HY·（X，OX），当X是n×n对称（分别为反对称矩阵）的复向量空间，Y是由任意固定秩的矩阵组成的GL-轨道的闭包。我们描述了局部上同调模的D-模合成因子，并根据广义二项式系数显式地计算它们的重数。我们的工作的一个结果是一个公式的上同调维数的理想，甚至未成年人的一般对称矩阵：在奇未成年人的情况下，这是由巴里在20世纪90年代。我们工作的另一个结果是，我们得到了局部上同调模分解为不可约GL-表示的描述（当X是m×n矩阵的向量空间时的类似问题在作者的早期工作中已经处理过）。
We compute the local cohomology modules HY•(X,OX) in the case when X is the complex vector space of n×n symmetric (respectively, skew‐symmetric matrices) and Y is the closure of the GL ‐orbit consisting of matrices of any fixed rank, for the natural action of the general linear group GL on X . We describe the D ‐module composition factors of the local cohomology modules, and compute their multiplicities explicitly in terms of generalized binomial coefficients. One consequence of our work is a formula for the cohomological dimension of ideals of even minors of a generic symmetric matrix: in the case of odd minors, this was obtained by Barile in the 1990s. Another consequence of our work is that we obtain a description of the decomposition into irreducible GL ‐representations of the local cohomology modules (the analogous problem in the case when X is the vector space of m×n matrices was treated in earlier work of the authors).