Proof of the BMR conjecture for \(G_{20}\) and \(G_{21}\)

DOI10.1016/j.jsc.2017.11.015zbMath1502.20004arXiv1701.09017OpenAlexW2583683745WikidataQ122863671 ScholiaQ122863671MaRDI QIDQ1756999

Ivan Marin

Publication date: 28 December 2018

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.09017

zbMATH Keywords

Hecke algebrascomplex reflection groupsBroué-Malle-Rouquier conjectureGröbner basis computations

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items

The freeness and trace conjectures for parabolic Hecke subalgebras ⋮ The BMM symmetrising trace conjecture for the exceptional 2-reflection groups of rank 2 ⋮ Hecke algebras of normalizers of parabolic subgroups ⋮ Defect in cyclotomic Hecke algebras ⋮ Geodesic normal forms and Hecke algebras for the complex reflection groups \(G(de, e, n)\) ⋮ BMR Freeness for Icosahedral Family ⋮ The principal block of a \(\mathbb{Z}_{\ell}\)-spets and Yokonuma type algebras ⋮ The BMM symmetrising trace conjecture for groups \(G_{4}\), \(G_{5}\), \(G_{6}\), \(G_{7}\), \(G_{8}\) ⋮ A computational approach to Shephard groups

Uses Software

• GBNP

Cites Work

• Unnamed Item
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• The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group \(G_{26}\).
• The BMR freeness conjecture for the first two families of the exceptional groups of rank 2
• A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
• Representation theory of a Hecke algebra of \(G(r,p,n)\)
• The cubic Hecke algebra on at most 5 strands.
• Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups.
• The BMR freeness conjecture for the 2-reflection groups
• The BMR freeness conjecture for the tetrahedral and octahedral families