Certain imprimitive reflection groups and their generic versions

DOI10.1090/S0002-9947-02-02941-0zbMath1033.20039OpenAlexW1486779769MaRDI QIDQ2781400

Jian-yi Shi

Publication date: 19 March 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-02-02941-0

zbMATH Keywords

Hecke algebraspresentationsaffine Weyl groupsaffine root systemsimprimitive reflection groups

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items

Interval garside structures related to the affine Artin groups of type \(\widetilde{A}\) ⋮ A note on fully commutative elements in complex reflection groups ⋮ Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups ⋮ Formula for the reflection length of elements in the group \(G(m,p,n)\). ⋮ Braid groups of imprimitive complex reflection groups. ⋮ Spectra of Cayley graphs of complex reflection groups ⋮ Simple Root Systems and Presentations for Certain Complex Reflection Groups ⋮ The Hurwitz action in complex reflection groups ⋮ Gröbner–Shirshov bases for congruence classes of complex reflection groups ⋮ A note on the Hurwitz action on reflection factorizations of Coxeter elements in complex reflection groups ⋮ Congruence classes of presentations for the complex reflection groups \(G(m,1,n)\) and \(G(m,m,n)\).

Cites Work

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• The Kazhdan-Lusztig cells in certain affine Weyl groups
• Root systems and length functions
• Affine Hecke Algebras and Their Graded Version
• Complex reflection groups
• Finite complex reflection groups
• Conjugacy relation on Coxeter elements