Generalisations of the Tits representation.
Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
We construct a subalgebra of dimension of the group algebra of the Weyl group of type containing its usual Solomon algebra and the one of : is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to . In an appendix, P. Baumann and C. Hohlweg present in an explicit and...
Generalized Induction of Kazhdan-Lusztig cells
Following Lusztig, we consider a Coxeter group together with a weight function. Geck showed that the Kazhdan-Lusztig cells of are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of 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 are cells in the whole group, and we decompose the affine Weyl group of type into left...
Generating series for the Coxeter groups and applications.
Geodesic automation and growth functions for Artin groups of finite type.
Geometrically constructed bases for homology of non-crossing partition lattices.
Geometry and analytic theory of Frobenius manifolds.
Green functions and a conjecture of Geck and Malle.
Growth of planar Coxeter groups, P.V. numbers, and Salem numbers.