Schubert calculus and equivariant cohomology of grassmannians
Schubert calculus and equivariant cohomology of grassmannians
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舒伯特微积分和格拉斯曼函数的等变上同调
DOI：
10.1016/j.aim.2007.09.014
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
D. Laksov
中科院分区：
文献类型：
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作者：
D. Laksov
我们给出了格拉斯曼函数等变上同调的描述，将该理论置于格拉斯曼函数上同调理论的通用框架中。由此我们得到了等变上同调的形式体系，其中等变舒伯特微积分、基定理、Pieri公式和Giambelli公式的基本结果可以通过改变基从一般框架的相应结果中得到。为了表明我们的形式主义反映了格拉斯曼函数的几何学，我们将我们的理论与 A. Knutson 和 T. Tao 对格拉斯曼函数的等变上同调的处理联系起来。
We give a description of equivariant cohomology of grassmannians that places the theory into a general framework for cohomology theories of grassmannians. As a result we obtain a formalism for equivariant cohomology where the basic results of equivariant Schubert calculus, the basis theorem, Pieri's formula and Giambelli's formula can be obtained from the corresponding results of the general framework by a change of basis. In order to show that our formalism reflects the geometry of grassmannians we relate our theory to the treatment of equivariant cohomology of grassmannians by A. Knutson and T. Tao.