Polynomial functions and wreath products

Coupled Cells: Wreath Products and Direct Products

In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...

Representation Zeta Functions of Wreath Products with Finite Groups

Let G be a group which has a finite number hn(G) of irreducible linear representations in GLn(C) for all n ≥ 1. Let ζ(G, s) = P∞ n=1 hn(G)n −s be its representation zeta function. First, in case G = H oXQ is a permutational wreath product with respect to a permutation group Q on a finite set X, we establish a formula for ζ(G, s) in terms of the zeta functions of H and of subgroups of Q, and of ...

The Wreath Products

Rooted Wreath Products

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...

Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions

Abstract. We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ ≀ Sn and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf ...