Let G be the group with Borel subgroup B, associated to a Kac-Moody Lie algebra [unk] (with Weyl group W and Cartan subalgebra [unk]). Then H*(G/B) has, among others, four distinguished structures (i) an algebra structure, (ii) a distinguished basis, given by the Schubert cells, (iii) a module for W, and (iv) a module for Hecke-type operators Aw, for w [unk] W. We construct a ring R, which we refer to as the nil Hecke ring, which is very simply and explicitly defined as a functor of W together with the W-module [unk] alone and such that all these four structures on H*(G/B) arise naturally from the ring R.
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机译：令G为Borel子组B的组，该子组与Kac-Moody Lie代数[unk]相关联（Weyl组W和Cartan子代数[unk]）。那么H * （G / B）除其他外，具有四个不同的结构（i）代数结构，（ii）由舒伯特单元给出的特殊基础，（iii）W的模块，以及（iv）用于W [unk] W的Hecke型算子Aw的模块。我们构造了一个环R，我们将其称为nil Hecke环，该环非常简单且明确地定义为W的函子仅使用W-module [unk]，并且 H * （ G / B ）上的所有这四个结构自然都来自环 R 。
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