We study the back stable Schubert calculus of the infinite flag variety. Our main results are:

• – a formula for back stable (double) Schubert classes expressing them in terms of a symmetric function part and a finite part;

• – a novel definition of double and triple Stanley symmetric functions;

• – a proof of the positivity of double Edelman–Greene coefficients generalizing the results of Edelman–Greene and Lascoux–Schützenberger;

• – the definition of a new class of bumpless pipedreams, giving new formulae for double Schubert polynomials, back stable double Schubert polynomials, and a new form of the Edelman–Greene insertion algorithm;

• – the construction of the Peterson subalgebra of the infinite nilHecke algebra, extending work of Peterson in the affine case;

• – equivariant Pieri rules for the homology of the infinite Grassmannian;

• – homology divided difference operators that create the equivariant homology Schubert classes of the infinite Grassmannian.

我们研究了无限标志变种的后向稳定舒伯特演算。我们的主要结果是：

• –后向稳定（双）Schubert类的公式，用对称函数部分和有限部分表示它们；

• –双重和三次斯坦利对称函数的新颖定义；

• –证明了双重Edelman-Greene系数的正性，将Edelman-Greene和Lascoux-Schützenberger的结果推广了一般性；

• –定义了新的一类无扰动的流派梦，给出了双舒伯特多项式的新公式，后向稳定双舒伯特多项式，以及新形式的爱德曼-格林插入算法；

• –无限nilHecke代数的Peterson子代数的构造，扩展了仿射情况下Peterson的工作；

• –无限Grassmannian的同源性的等变Pieri规则；

• –均分除差算子，它创建无限草曼的等变均等Schubert类。