Related papers: Local recognition of reflection graphs on Coxeter …

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems,…

Guided by the ideas of chirality in the abstract polytope theory, the present paper aims to extend the concept to a more general setting of incidence geometries. The purpose of this paper is to explore the more general framework of thin…

When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d>1, one obtains a finite group G^d which is often the automorphism group of an abstract regular polytope. Building…

A characterization is given of finite groups $H$ that have skew-morphisms of order coprime to the order $|H|$, and their skew-morphisms. A complete classification is then given of the automorphism groups and the underlying graphs of…

We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that a non-spherical and non-affine Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly)…

This paper studies cluster algebras locally, by identifying a special class of localizations which are themselves cluster algebras. A `locally acyclic cluster algebra' is a cluster algebra which admits a finite cover (in a geometric sense)…

In this article, we establish some new combinatorial properties of cone types in Coxeter groups. Firstly, we show that for any element $x$ in a Coxeter group $W$ and root $\beta$ in its inversion set $\Phi(x)$, the set of elements $y \in W$…

In this paper, we classify reflexible regular Cayley maps for dihedral groups.

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

We survey the area of strongly regular graphs satisfying the 4-vertex condition and find several new families. We describe a switching operation on collinearity graphs of polar spaces that produces cospectral graphs. The obtained graphs…

We give a case-by-case description of the centralizers of involutions in finite Coxeter groups.

We prove a number of results about profinite completions of Coxeter groups. For example we prove Coxeter groups are good in the sense of Serre and that various splittings of Coxeter groups arising from actions on trees are detected by the…

We examine the cohomology and representation theory of a family of finite supergroup schemes of the form $(\mathbb G_a^-\times \mathbb G_a^-)\rtimes (\mathbb G_{a(r)}\times (\mathbb Z/p)^s)$. In particular, we show that a certain relation…

Let $G({\mathbb F}_{q})$ be a finite Chevalley group defined over the field of $q=p^{r}$ elements, and $k$ be an algebraically closed field of characteristic $p>0$. A fundamental open and elusive problem has been the computation of the…

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of commutative rings that includes the localizations of 1-generated…

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…

We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain…

Given a class of groups C, a group G is strongly accessible over C if there is a bound on the number of terms in a sequence L(1), L(2), ..., L(n) of graph of groups decompositions of G with edge groups in C such that L(1) is the trivial…

In this note we show that all reductive groups are clean in odd characteristic. In characteristic 2 there are two cuspidal local systems (one for $F_4$ and one for $E_8$) which can not be handled by our method.

It is known that splittings of finitely presented groups over 2-ended groups can be characterized geometrically. We show that this characterization does not extend to all finitely generated groups. Answering a question of Kleiner we show…