Related papers: Discrete Coxeter groups

We generalize earlier work of Fuertes and Gonz\'{a}lez-Diez as well as earlier work of Bauer, Catanese and Grunewald to Coxeter groups in general by classifying which of these are strongly real Beauville groups. As a consequence of this we…

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups…

We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a…

In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and…

This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remarkable negative curvature properties. The study of these…

In [LV] the authors defined a Hecke algebra action and a bar involution on a vector space spanned by the involutions in a Weyl group. In this paper we give a new definition of the Hecke algebra action and the bar operator which, unlike the…

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c,…

The lower central series of the rgiht-angled Coxeter group $RC_\mathcal K$ and the corresponding graded Lie algebra $L(RC_\mathcal K)$ associated with the lower central series of a right-angled Coxeter group are studied. Relations are…

Cycloids, hipocycloids and epicycloids have an often forgotten common property: they are homothetic to their evolutes. But what if use convex symmetric polygons as unit balls, can we define evolutes and cycloids which are genuinely…

In groups with involution a nonassociative product of elements is defined, which leads to the definition of a certain type of quasigroups. These quasigroups are represented by square tables of complex numbers, with inverses, which differ…

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 previous article we have defined an action of the Iwahori-Hecke algebra of a Coxeter group W on a free module with basis indexed by the involutions in W. In this paper we show that the specialization of this action at the parameter 0…

We study coherence of graph products and Coxeter groups and obtain many results in this direction.

We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants…

To every group of $I$-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the…

We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We…

We obtain two related characterizations of discrete quantum groups and discrete quantum groups of Kac type as allegorical group objects in the symmetric monoidal dagger category of quantum sets and relations, of interest to quantum…

We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…

In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse…