Related papers: Simply-laced Coxeter groups and groups generated b…

A finite subgroup of $GL(n,\mathbb C)$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniform combinatorial model is constructed for all…

We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such…

We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…

We provide examples of groups which are indecomposable by direct product, and more generally which are uniquely decomposable in direct products of indecomposable groups. Examples include Coxeter groups, for which we give an alternative…

Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y…

We refine the infinitesimal Hecke algebra associated to a 2-reflection group into a $\Z/2\Z$-graded Lie algebra, as a first step towards a global understanding of a natural $\mathbbm{N}$-graded object. We provide an interpretation of this…

Let $\Sigma$ be the Davis complex for a Coxeter system (W,S). The automorphism group G of $\Sigma$ is naturally a locally compact group, and a simple combinatorial condition due to Haglund--Paulin determines when G is nondiscrete. The…

In this article, we give a short algebraic proof that all closed intervals in a $\gamma$-Cambrian semilattice $\mathcal{C}_{\gamma}$ are trim for any Coxeter group $W$ and any Coxeter element $\gamma\in W$. This means that if such an…

Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the…

We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, providing groups that exhibit various combinations of properties:…

Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated, and the finite $\frac{3}{2}$-generated…

Let $Q$ be an acyclic quiver and $\Lambda$ be the complete preprojective algebra of $Q$ over an algebraically closed field $k$. To any element $w$ in the Coxeter group of $Q$, Buan, Iyama, Reiten and Scott have introduced and studied in…

We introduce a Brauer type algebra $B_G (\Upsilon) $ associated with every pseudo reflection group and every Coxeter group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized…

In this article, given two finite simplicial graphs $\Gamma_1$ and $\Gamma_2$, we state and prove a complete description of the possible morphisms $C(\Gamma_1) \to C(\Gamma_2)$ between the right-angled Coxeter groups $C(\Gamma_1)$ and…

We classify surjective lattice homomorphisms $W\to W'$ between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences $\Theta$ on $W$ such that the quotient $W/\Theta$ is isomorphic to $W'$. Surprisingly,…

Given a group acting cellularly and cocompactly on a simply-connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the "perimeter method". As an…

We introduce the notion of 321-avoiding permutations in the affine Weyl group $W$ of type $A_{n-1}$ by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey,…

Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…

In this article we give an self contained existence proof for J. Conway's sporadic simple group Co_1 [4] using the second author's algorithm [14] constructing finite simple groups from irreducible subgroups of GL_n(2). Here n = 11 and the…

The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ is a finite dimensional real vector space, which have the following property \SP{}: the family of convex hulls of $G$-orbits is a semigroup with respect…