The BMR freeness conjecture for the first two families of the exceptional groups of rank 2
The freeness conjecture of \textit{M. Broué} et al. [J. Reine Angew. Math. 500, 127--190 (1998; Zbl 0921.20046)] (briefly BMR conjecture) states that the generic Hecke algebra for the complex reflection group \(W\) is free of finite rank. The BMR conjecture is still open for 14 cases, which cover almost all the exceptional complex reflection groups of rank 2. In this paper, the author proves the conjecture for 9 of these remaining cases, giving a basis similar to the classical case of the finite Coxeter groups. In particular, the main theorem (Theorem 5.1) states that the BMR conjecture holds for all the groups belonging to the tetrahedral and octahedral families.
Broué-Malle-Rouquier freeness conjecture
scientific article; zbMATH DE number 6673216