The cubic Hecke algebra on at most 5 strands.
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Publication:1940208
DOI10.1016/j.jpaa.2012.04.013zbMath1266.20006arXiv1110.6621OpenAlexW2007017305MaRDI QIDQ1940208
Publication date: 6 March 2013
Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1110.6621
Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55)
Related Items (27)
Universal deformations of the finite quotients of the braid group on 3 strands. ⋮ Markov traces on the Funar algebra ⋮ The freeness and trace conjectures for parabolic Hecke subalgebras ⋮ Lattice extensions of Hecke algebras ⋮ A maximal cubic quotient of the braid algebra. I. ⋮ The BMM symmetrising trace conjecture for the exceptional 2-reflection groups of rank 2 ⋮ The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group \(G_{26}\). ⋮ On the representation theory of braid groups. ⋮ Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\) ⋮ 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 ⋮ Proof of the Broué-Malle-Rouquier conjecture in characteristic zero (after I. Losev and I. Marin-G. Pfeiffer) ⋮ The BMR freeness conjecture for the 2-reflection groups ⋮ A cubic defining algebra for the Links-Gould polynomial ⋮ On ternary quotients of cubic Hecke algebras. ⋮ A counter-example to Martino's conjecture about generic Calogero-Moser families. ⋮ The BMR freeness conjecture for the tetrahedral and octahedral families ⋮ The BMR freeness conjecture for the first two families of the exceptional groups of rank 2 ⋮ A quotient of the Artin braid groups related to crystallographic groups ⋮ Proof of the BMR conjecture for \(G_{20}\) and \(G_{21}\) ⋮ The BMM symmetrising trace conjecture for groups \(G_{4}\), \(G_{5}\), \(G_{6}\), \(G_{7}\), \(G_{8}\) ⋮ Braid group action on projective quantum \(\mathfrak{sl}(2)\) modules ⋮ A computational approach to Shephard groups ⋮ Unnamed Item ⋮ Fusion for the Yang-Baxter equation and the braid group
Cites Work
- On ternary quotients of cubic Hecke algebras.
- Einige endliche Faktorgruppen der Zopfgruppen
- A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
- On the quotients of cubic Hecke algebras
- Representation theory of a Hecke algebra of \(G(r,p,n)\)
- Krammer representations for complex braid groups.
- A cubic defining algebra for the Links-Gould polynomial
- Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups.
- Polynomial invariants of links satisfying cubic skein relations
- Groups Generated by Unitary Reflections of Period Two
- Representations of the braid group \(B_3\) and of \(\text{SL}(2,\mathbb{Z})\).
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