Cyclotomic Solomon Algebras

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dc.creatorMathas, Andrew
dc.creatorOrellana, Rosa C.
dc.date2008-01-07
dc.date2008-05-09
dc.date.accessioned2026-07-07T09:37:40Z
dc.date.available2026-07-07T09:37:40Z
dc.descriptionThis paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type $G(r,1,n)$. As with the Solomon descent algebra, our algebra has a basis given by sums of `distinguished' coset representatives for certain `reflection subgroups'. We explicitly describe the structure constants with respect to this basis and show that they are polynomials in $r$. This allows us to define a deformation, or $q$-analogue, of these algebras which depends on a parameter $q$. We determine the irreducible representations of all of these algebras and give a basis for their radicals. Finally, we show that the direct sum of cyclotomic Solomon algebras is canonically isomorphic to a concatenation Hopf algebra.
dc.identifierhttps://arxiv.org/abs/0801.0874
dc.identifierhttp://arxiv.org/abs/0801.0874
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160541
dc.subjectCombinatorics
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject16W30; 20C05; 05E15
dc.titleCyclotomic Solomon Algebras
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