# Formal affine Demazure and Hecke algebras of Kac-Moody root systems

## TL;DR

This paper introduces formal affine Demazure and Hecke algebras for Kac-Moody root systems, extending known finite root system results to the infinite-dimensional case with new structural theorems.

## Contribution

It defines these algebras for Kac-Moody systems and proves their structural properties, generalizing finite root system theories.

## Key findings

- Established presentations with generators and relations
- Proved coproduct and product structures
- Developed filtrations and multiplication formulas

## Abstract

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