Specht Modules and Branching Rules for Ariki-Koike Algebras

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dc.creatorDu, J.
dc.creatorRui, H.
dc.date1999-02-15
dc.date.accessioned2026-07-07T05:27:55Z
dc.date.available2026-07-07T05:27:55Z
dc.descriptionSpecht modules for an Ariki-Koike algebra have been investigated recently in the context of cellular algebras. Thus, these modules are defined as quotient modules of certain ``permutation'' modules, that is, defined as ``cell modules'' via cellular bases. We shall introduce in this paper Specht modules for an Ariki-Koike algebra as submodules of those ``permutation'' modules and investigate their basic properties such as Standard Basis Theorem and the ordinary Branching Theorem, generalizing several classical constructions for type $A$. The second part of the paper moves on looking for Kleshchev's branching rules for Specht and irreducible modules over an Ariki-Koike algebra. We shall restrict to the case where the Ariki-Koike algebra has a semi-simple bottom. With a recent work of Ariki on the classification of irreducible modules, we conjecture that the results should be true in general if $l$-regular multipartitions are replaced by Kleshchev's multipartitions. We point out that our approach is independent of the use of cellular bases.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/9902088
dc.identifierhttp://arxiv.org/abs/math/9902088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78106
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject16G99, 20C20, 20C30, 20G05
dc.titleSpecht Modules and Branching Rules for Ariki-Koike Algebras
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