We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities for the Coxeter polynomials of the trees respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least where .
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.
We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.
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...
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...