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.

中文翻译：

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通过非对称六顶点模型的圆柱 Hecke 字符和 Gromov-Witten 不变量

我们在 Hecke 代数的 Grothendieck 环中构造了一个无限维正子代数族，当被视为关于归纳和限制函子的 Hopf 代数时。这些子代数具有作为结构常数的 Grassmannians 的 3 点属零 Gromov-Witten 不变量，并且被我们称为圆柱 Hecke 字符的东西所覆盖，这是一组特定的虚拟字符，我们给出了几个明确的组合公式来计算它们。其中一个表达式是对不可约的 Hecke 字符的 Ram 公式的概括，并使用了圆柱形破碎的边缘钩子画面。我们表明，后者在圆柱方格上与所谓的“冰配置”双射，这定义了统计力学中的非对称六顶点模型。