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General construction of non-dense disjoint iteration groups on the circle

Krzysztof Ciepliński (2005)

Czechoslovak Mathematical Journal

Let = { F v 𝕊 1 𝕊 1 , v V } be a disjoint iteration group on the unit circle 𝕊 1 , that is a family of homeomorphisms such that F v 1 F v 2 = F v 1 + v 2 for v 1 , v 2 V and each F v either is the identity mapping or has no fixed point ( ( V , + ) is a 2 -divisible nontrivial Abelian group). Denote by L the set of all cluster points of { F v ( z ) , v V } for z 𝕊 1 . In this paper we give a general construction of disjoint iteration groups for which L 𝕊 1 .

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

We construct a subalgebra Σ ( W n ) of dimension 2 · 3 n - 1 of the group algebra of the Weyl group W n of type B n containing its usual Solomon algebra and the one of 𝔖 n : Σ ( W n ) is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras Σ ( W n ) Z Irr ( W n ) . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to W n . In an appendix, P. Baumann and C. Hohlweg present in an explicit and...

Generalized Induction of Kazhdan-Lusztig cells

Jérémie Guilhot (2009)

Annales de l’institut Fourier

Following Lusztig, we consider a Coxeter group W together with a weight function. Geck showed that the Kazhdan-Lusztig cells of W are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of W which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of W are cells in the whole group, and we decompose the affine Weyl group of type G into left...

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