非对称六顶点模型下的Adherdric Hecke特征标和Gromov-Witten不变量
Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model
摘要：
我们构造了一族无限维的正子余代数的Grothendieck环的Hecke代数，当被视为一个Hopf代数的诱导和限制函子。这些子余代数的结构常数的3点属零Gromov-Witten不变量的格拉斯曼和跨越我们所谓的圆柱Hecke字符，一组特定的虚拟字符的计算，我们给出了几个明确的组合公式。这些表达式之一是一个概括的拉姆公式的不可约Hecke字符和使用圆柱形打破边缘钩tableaux。我们发现，后者是在双射与所谓的“冰配置”的圆柱形正方形晶格，定义了不对称的六顶点模型在统计力学。我们的建设的一个关键组成部分是一个扩展的玻色子费米子对应Hecke代数，并采用后者，我们找到新的表达式京的顶点运营商的Hall-Littlewood功能的六顶点转移矩阵的无限平面晶格。
英文摘要：
We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as structure constants the 3-point genus zero Gromov-Witten invariants of Grassmannians and are spanned by what we call cylindric Hecke characters, a particular set of virtual characters for whose computation we give several explicit combinatorial formulae. One of these expressions is a generalisation of Ram's formula for irreducible Hecke characters and uses cylindric broken rim hook tableaux. We show that the latter are in bijection with so-called `ice configurations' on a cylindrical square lattice, which define the asymmetric six-vertex model in statistical mechanics. A key ingredient of our construction is an extension of the boson-fermion correspondence to Hecke algebras and employing the latter we find new expressions for Jing's vertex operators of Hall-Littlewood functions in terms of the six-vertex transfer matrices on the infinite planar lattice.
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