We define the formal affine Demazure algebra and a formal affine Hecke algebra associated to a Kac-Moody root system. We prove structure theorems for these algebras, and use them to extend several results and constructions (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root systems.

中文翻译：

---

Kac-Moody根系统的形式仿射Demazure和Hecke代数

我们定义了与Kac-Moody根系统相关的形式仿射Demazure代数和形式仿射Hecke代数。我们证明了这些代数的结构定理，并用它们扩展了以前已知的几种结果和结构（以生成器和关系，副产品和乘积结构表示，通过Bott-Samelson类的维数滤波，根多项式和乘法公式表示）用于有限的根系统。