%0 Journal Article
%T Cyclotomic Solomon Algebras
%A Andrew Mathas
%A Rosa C. Orellana
%J Mathematics
%D 2008
%I arXiv
%X This 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.
%U http://arxiv.org/abs/0801.0874v2