A Reducibility Theorem ofG(m, 1,r) and Its Application to Trace Functions on Ariki–Koike Algebras

DOI10.1080/00927870701776730zbMath1152.20036OpenAlexW2029018274MaRDI QIDQ3510062

Chi Kin Mak

Publication date: 26 June 2008

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870701776730

zbMATH Keywords

Hecke algebrasreduced expressionsconjugacy classescharactersAriki-Koike algebrascomplex reflection groupstrace functionsGeck-Pfeiffer reducibility theorem

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Cites Work

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• Representation theory of the 0-Hecke algebra
• A Frobenius formula for the characters of the Hecke algebras
• On the irreducible characters of Hecke algebras
• 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 \(G(e,1,n)\)
• Modified Ariki-Koike algebras and cyclotomic \(q\)-Schur algebras.
• The minimal basis for the centre of an Iwahori-Hecke algebra
• A Frobenius formula for the characters of Ariki-Koike algebras
• Centralizers of Iwahori-Hecke algebras
• Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)
• Quasi-parabolic subgroups of \(G(m,1,r)\).

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