We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober classes of Schubert varieties in general homogeneous spaces G / P . While these classes do not depend on any choice, they depend on a set of new variables. For the definition of our classes we calculate multiplicities of some divisors in Schubert varieties, which were only known for full flag varieties before. Our approach leads to a simple recursions for the elliptic classes. Comparing this recursion with R-matrix recursions of the so-called elliptic weight functions of Rimanyi–Tarasov–Varchenko we prove that weight functions represent elliptic classes of Schubert varieties.

中文翻译：

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舒伯特变体的椭圆类

我们在椭圆舒伯特微积分中引入了新概念：一般齐次空间 G / P 中舒伯特变体的（扭曲的）鲍里索夫-利布戈伯类。虽然这些类不依赖于任何选择，但它们依赖于一组新变量。为了定义我们的类，我们计算了 Schubert 变体中一些除数的重数，这些除数以前只知道 full flag 变体。我们的方法导致椭圆类的简单递归。将此递归与 Rimanyi-Tarasov-Varchenko 所谓的椭圆权重函数的 R 矩阵递归进行比较，我们证明权重函数代表 Schubert 变体的椭圆类。