The BMR freeness conjecture for the 2-reflection groups

TL;DR

This paper proves the BMR freeness conjecture for Hecke algebras linked to primitive complex 2-reflection groups with a single conjugacy class of reflections, advancing understanding in algebraic structures.

Contribution

It establishes the conjecture's validity specifically for primitive complex 2-reflection groups with one conjugacy class of reflections, a case previously unresolved.

Findings

Confirmed the BMR freeness conjecture for these groups

Extended the class of groups for which the conjecture holds

Provided new algebraic insights into Hecke algebras

Abstract

We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections.