Cyclotomic Solomon algebras

• Autores: Andrew Mathas, Rosa C. Orellana
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 2, 2008, págs. 450-487
• Idioma: inglés
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• Resumen

  • 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.