Quantum Bruhat graph and Schubert polynomials
Quantum Bruhat graph and Schubert polynomials
复制标题
量子 Bruhat 图和舒伯特多项式
DOI：
10.1090/s0002-9939-04-07614-2
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发表时间：
2002
影响因子：
0.8
通讯作者：
A. Postnikov
中科院分区：
文献类型：
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作者：
A. Postnikov
量子Bruhat图是由Bruhat阶覆盖关系构成的图的推广，它自然地与G/B的量子上同调环有关。我们增强了富尔顿和伍德沃德的结果表明，最小单项式的量子参数中发生的量子产品的两个舒伯特类有一个简单的解释，在这个图中的有向路径。我们定义了路径舒伯特多项式，它是最近由勒纳特和Sottile引入的斜舒伯特多项式的量子上同调类似物。它们由A型量子Bruhat图中的路和给出。旗流形的3点Gromov-Witten不变量用这些多项式表示。这种构造给出了两个舒伯特类的量子乘积中出现的量子参数中的所有单项式的集合的组合描述。
The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton and Woodward by showing that the minimal monomial in the quantum parameters that occurs in the quantum product of two Schubert classes has a simple interpretation in terms of directed paths in this graph. We define path Schubert polynomials, which are quantum cohomology analogs of skew Schubert polynomials recently introduced by Lenart and Sottile. They are given by sums over paths in the quantum Bruhat graph of type A. The 3-point Gromov-Witten invariants for the flag manifold are expressed in terms of these polynomials. This construction gives a combinatorial description for the set of all monomials in the quantum parameters that occur in the quantum product of two Schubert classes.
DOI：
--
发表时间：
2005
期刊：
影响因子：
--
作者：
T. Kobayashi;T. Oshima
通讯作者：
T. Oshima