Proof of the Brou\'e-Malle-Rouquier conjecture in characteristic zero (after I. Losev and I. Marin - G. Pfeiffer)

TL;DR

This paper presents a detailed exposition of the proof of the Broué-Malle-Rouquier conjecture, confirming that Hecke algebras of finite complex reflection groups are free modules over their parameter algebras in characteristic zero.

Contribution

It provides a comprehensive explanation of the proof by Losev and Marin-Pfeiffer, establishing the conjecture's validity in characteristic zero and large positive characteristic.

Findings

Proof confirms the conjecture in characteristic zero

Hecke algebras are free modules over parameter algebras

Supports the conjecture in large positive characteristic

Abstract

In 1998 Brou\'e, Malle and Rouquier conjectured that the Hecke algebra of a finite complex reflection group W is a free module over the algebra of parameters of rank |W|. We give an exposition of a proof of this conjecture in characteristic zero (and sufficiently large positive characteristic), due to I. Losev and I. Marin - G. Pfeiffer.