We prove that the sheaf Euler characteristic of the product of a Schubert class and an opposite Schubert class in the quantum K-theory ring of a (generalized) flag variety G/P is equal to \(q^d\), where d is the smallest degree of a rational curve joining the two Schubert varieties. This implies that the sum of the structure constants of any product of Schubert classes is equal to 1. Along the way, we provide a description of the smallest degree d in terms of its projections to flag varieties defined by maximal parabolic subgroups.

中文翻译：

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标记变体的量子K理论中的欧拉特性

我们证明（广义）标记变种G / P的量子K-理论环中Schubert类和相反Schubert类乘积的捆Euler特征等于\（q ^ d \），其中d为连接两个舒伯特品种的有理曲线的最小度。这意味着Schubert类的任何乘积的结构常数之和等于1。一路上，我们根据最小抛物线对由最大抛物子组定义的标志变数的投影，提供了最小度d的描述。