Geodesic normal forms and Hecke algebras for the complex reflection groups G(de, e, n)

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Neaime, Georges¹ 

[1] Univ Bielefeld, Fak Math, Univ Str 25, D-33615 Bielefeld, Germany

关键词: Complex reflection groups;    Complex braid groups;    Geodesic normal forms;    Hecke algebras;    BMR freeness conjecture;   

DOI  :  10.1016/j.jpaa.2020.106500

来源: Elsevier

【 摘 要 】

We establish geodesic normal forms for the general series of complex reflection groups G(de, e, n) by using the presentations of Corran-Picantin and Corran- Lee-Lee of G(e, e, n) and G(de, e, n) for d > 1, respectively. This requires the elaboration of a combinatorial technique in order to explicitly determine minimal word representatives of the elements of G(de, e, n). Using these geodesic normal forms, we construct natural bases for the Hecke algebras associated with the complex reflection groups G(e, e, n) and G(d, 1, n). As an application, we obtain a new proof of the BMR freeness conjecture for these groups. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free