A generalization of solomon’s algebra for hyperoctahedral groups and other wreath products

Abstract

Abstract In this paper we give a combinatorial rule to compute the composition of two convolution products of endomorphisms of a free associative algebra and deduce the construction of a subalgebra of QB n (the group algebra of Hyperoctahedral group) which contains the descent algebra X#". We also deduce a proof of the multiplication rule in the algebra ∑QB n- Finally, we generalize this construction to other wreath products of symmetric groups by abelian groups. *Invited visitor at Université du Québec á Montréal, partially supported by the Dottorato di Ricerca in Matematica, Universitá di Roma La Sapienza †Supported by NSERC Canada *Invited visitor at Université du Québec á Montréal, partially supported by the Dottorato di Ricerca in Matematica, Universitá di Roma La Sapienza †Supported by NSERC Canada Notes *Invited visitor at Université du Québec á Montréal, partially supported by the Dottorato di Ricerca in Matematica, Universitá di Roma La Sapienza †Supported by NSERC Canada