二聚体、晶体和量子Kostka数
Dimers, crystals and quantum Kostka numbers
摘要：
我们与蜂窝状二聚体配置的圆柱体上的计数Kirillov-Reshetikhin晶体图中的某些顶点的计数。我们证明了这些二聚体构型产生了Grassmannian小量子上同调环的量子Kostka数，即Schubert类与不同的Chern类反复相乘时的展开系数.这使得人们可以推导出Gromov-Witten不变量的求和规则。
英文摘要：
We relate the counting of honeycomb dimer configurations on the cylinder to the counting of certain vertices in Kirillov-Reshetikhin crystal graphs. We show that these dimer configurations yield the quantum Kostka numbers of the small quantum cohomology ring of the Grassmannian, i.e. the expansion coefficients when multiplying a Schubert class repeatedly with different Chern classes. This allows one to derive sum rules for Gromov-Witten invariants.
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