Proof of the BMR conjecture for G20 and G21. (May 2019)

• Record Type: Journal Article
• Authors: Marin, Ivan
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 1
• Page End: 14
• Publication Date: 2019-05
• Subjects: Broué–Malle–Rouquier conjecture -- Gröbner basis computations -- Hecke algebras -- Complex reflection groups; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.11.015
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We prove two new cases of the Broué–Malle–Rouquier freeness conjecture for the Hecke algebras associated to complex reflection groups, using methods inspired by non-commutative Gröbner bases. These two cases are the complex reflection groups of rank 2 called G 20 and G 21 in the Shephard and Todd classification. This reduces the number of remaining unproven cases to 3.