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

DOI10.1016/J.JPAA.2020.106500OpenAlexW3043149868MaRDI QIDQ2196358

Georges Neaime

Publication date: 28 August 2020

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12053

zbMATH Keywords

Hecke algebrascomplex reflection groupscomplex braid groupsBMR freeness conjecturegeodesic normal forms

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36)

Cites Work

• The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group \(G_{26}\).
• A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
• Reduced words and a length function for \(G(e,1,n)\)
• Proof of the BMR conjecture for \(G_{20}\) and \(G_{21}\)
• Representation theory of a Hecke algebra of \(G(r,p,n)\)
• The cubic Hecke algebra on at most 5 strands.
• Braid groups of imprimitive complex reflection groups.
• The BMR freeness conjecture for the 2-reflection groups
• A new Garside structure for the braid groups of type (e, e, r )
• Cyclotomic quiver Hecke algebras and Hecke algebra of $G(r,p,n)$
• The BMR freeness conjecture for the tetrahedral and octahedral families
• BMR Freeness for Icosahedral Family
• Interval Garside structures for the complex braid groups 𝐵(𝑒,𝑒,𝑛)
• Finite Unitary Reflection Groups
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