Quantum cohomology rings of Grassmannians and total positivity
Quantum cohomology rings of Grassmannians and total positivity
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DOI：
10.1215/s0012-7094-01-11033-8
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发表时间：
2001-12
影响因子：
2.5
通讯作者：
K. Rietsch
中科院分区：
文献类型：
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作者：
K. Rietsch
给出了D.彼得森的确定量子上同调环的格拉斯曼与约化坐标环的某个子类的GLn。然后构造了这个子簇的全正部分，并给出了Schubert基元在全正点上的值的封闭公式。然后，我们使用开发的方法给一个新的证明公式的Vafa和Intriligator和Bertram的结构常数（Gromov-Witten不变量）。最后，我们利用这些Gromov-Witten不变量的正性证明了Schur多项式在单位根上的某些不等式。
We give a proof of a result of D. Peterson’s identifying the quantum cohomology ring of a Grassmannian with the reduced coordinate ring of a certain subvariety of GLn. The totally positive part of this subvariety is then constructed and we give closed formulas for the values of the Schubert basis elements on the totally positive points. We then use the developed methods to give a new proof of a formula of Vafa and Intriligator and Bertram for the structure constants (Gromov–Witten invariants). Finally, we use the positivity of these Gromov–Witten invariants to prove certain inequalities for Schur polynomials at roots of unity.