Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes
Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes
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加权格拉斯曼函数和加权舒伯特类的等变上同调
DOI：
10.1093/imrn/rnu003
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
T. Matsumura
中科院分区：
文献类型：
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作者：
Hiraku Abe;T. Matsumura
本文研究了由Corti-Reid引入的加权Grassmannian群wGr（d，n）的T_w-等变上同调，其中T_w是自然作用在wGr（d，n）上的n维环面.我们引入等变加权舒伯特类，并在我们表明，它们形成的基础上的等变上同调，我们给出了一个明确的公式结构常数就这个舒伯特基础。我们还找到了一个线性无关的子集{wu_1，...，wu_n}，使得这些结构常数是wu_i中具有非负系数的多项式，直到权重上的置换。
In this paper, we study the T_w-equivariant cohomology of the weighted Grassmannians wGr(d,n) introduced by Corti-Reid where T_w is the n-dimensional torus that naturally acts on wGr(d,n). We introduce the equivariant weighted Schubert classes and, after we show that they form a basis of the equivariant cohomology, we give an explicit formula for the structure constants with respect to this Schubert basis. We also find a linearly independent subset {wu_1,...,wu_n} of Lie(T_w)^* such that those structure constants are polynomials in wu_i's with non-negative coefficients, up to a permutation on the weights.