Formal Affine Demazure and Hecke Algebras of Kac-Moody Root Systems

Abstract

We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root systems. We prove the structure theorems of these algebras, hence, extending 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.

Equivariant oriented homology of the affine Grassmannian

“…In this section, we recall the construction of the formal affine Demazure algebra (FADA) for the affine root system. All the construction can be found in [CZZ20].…”

“…This is called the formal affine Demazure algebra (FADA) for the big torus. It is easy to see that XIw , w ∈ W a is a Q-basis of QWa , and it is proved in [CZZ20] that it is also a basis of the left Ŝ-module DWa . Note that W ⊂ DWa via the map…”