Related papers: Interval groups related to finite Coxeter groups I

We provide a complete description of the presentations of the interval groups related to quasi-Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group…

We consider presentations that were derived in \cite{BaumeisterNeaimeRees} for the interval groups associated with proper quasi-Coxeter elements of the Coxeter group $W(D_n)$. We use combinatorial methods to derive alternative presentations…

We classify two-dimensional right-angled Coxeter groups that are quasiisometric to a right-angled Artin group defined by a tree, and show that when this is true the right-angled Coxeter group actually contains a visible finite index…

Let $C(T)$ be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either $B_n$ or $D_n$. Let $C_Y(T)$ be a natural quotient of $C(T)$, and if $C(T)$ is simply-laced (which means all the relations…

A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the…

We apply the techniques of symmetric generation to establish the standard presentations of the finite simply laced irreducible finite Coxeter groups, that is the Coxeter groups of types An, Dn and En, and show that these are naturally…

The author is mainly interest in the Gr\"{o}bner-Shirshov bases of finite Coxeter groups. It is known that the finite Coxeter groups are classified in terms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mention that the…

We situate the noncrossing partitions associated to a finite Coxeter group within the context of the representation theory of quivers. We describe Reading's bijection between noncrossing partitions and clusters in this context, and show…

In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing…

In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type $D_n$, and study the combinatorics of these subsets, revealing hidden structures. (We do not consider type $A_n$ first,…

Let W be an irreducible finitely generated Coxeter group. The geometric representation of W in GL(V) provides a discrete embedding in the orthogonal group of the Tits form (the associated bilinear form of the Coxeter group). If the Tits…

In a recent paper, Barot and Marsh presented an explicit construction of presentation of a finite Weyl group by any seed of corresponding cluster algebra, i.e. by any diagram mutation-equivalent to an orientation of a Dynkin diagram with…

In this paper we describe a family of isomorphism invariants of a finitely generated Coxeter group W. Each of these invariants is the isomorphism type of a quotient group W/N of W by a characteristic subgroup N. The virtue of these…

We define ``star reducible'' Coxeter groups to be those Coxeter groups for which every fully commutative element (in the sense of Stembridge) is equivalent to a product of commuting generators by a sequence of length-decreasing star…

We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex…

The aim of this note is to show that the cycle decomposition of elements of the symmetric group admits a quite natural formulation in the framework of dual Coxeter theory, yielding a generalization of it to the family of so-called parabolic…

The irreducible euclidean Coxeter groups that naturally act geometrically on euclidean space are classified by the well-known extended Dynkin diagrams and these diagrams also encode the modified presentations that define the irreducible…

The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as such it has a presentation as quiver with relations. In recent work, we have developed a combinatorial framework which allows us to systematically compute such a…

Artin groups are a natural generalization of braid groups and are well-understood in certain cases. Artin groups are closely related to Coxeter groups. There is a faithful representation of a Coxeter group $W$ as a linear reflection group…

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such…