Major indices and perfect bases for complex reflection groups.
Minimal length coset representatives for quotients of parabolic subgroups in Coxeter groups
In questo lavoro viene trovata un'espressione esplicita per i rappresentanti dei laterali di sottogrupi parabolici di gruppi di Coxeter aventi lunghezza minima: dato un sistema di Coxeter ed un suo sottogruppo parabolico , con , si determina esplicitamente in ogni laterale di un elemento avente lunghezza minima. Nella sezione 2 trattiamo i casi classici, i.e. , e . Dopo ciò, nella sezione 3, diamo una procedura per risolvere il problema nei restanti casi eccezionali, insieme a qualche...
More on the girth of graphs on Weyl groups
The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.
Multiple Dirichlet series over rational function fields
New insights into viral architecture via affine extended symmetry groups.
Noncrossing partitions, clusters and the Coxeter plane.
Non-gatherable triples for non-affine root systems.
On a four-generator Coxeter group.
On a subgroup of the affine Weyl group .
On an open problem of Green and Losonczy: exact enumeration of freely braided permutations.
On connectedness of graphs on direct product of Weyl groups
In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
On connectedness of graphs on Weyl groups of type ()
On irreducible, infinite, nonaffine Coxeter groups
The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. We also prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine...
On Outer Automorphism Groups of Coxeter Groups.
On special pieces in the unipotent variety.
On the “Bruhat graph” of a Coxeter system
On the excedance number of colored permutation groups.
On the graph on a Weyl group being an interval graph.
On the inverse braid and reflection monoids of type .
On the reflection representation in Springer's theory.