Geodesic Normal Forms and Hecke Algebras for the Complex Reflection Groups G(de,e,n)
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Publication:6308915
DOI10.1016/J.JPAA.2020.106500arXiv1810.12053MaRDI QIDQ6308915
Publication date: 29 October 2018
Abstract: 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.
Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55)
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