Related papers: Coxeter groups as Beauville groups
Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the…
A Beauville surface (of unmixed type) is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the product, where G preserves the two curves and their…
In the paper "Aquino, C., Jim\'enez, R., Mijangos, M., Morales Mel\'endez, Q.: On Invariant (co)homology of a group, preprint" are introduced two groups generated by the orbits of an action of a group on another group by automorphisms. One…
We find asymptotic lower bounds for the numbers of both Beauville and non-Beauville $2$-generator finite $p$-groups of a fixed order, which turn out to coincide with the best known asymptotic lower bound for the total number of…
It is known that Euler numbers, defined as the Taylor coefficients of the tangent and secant functions, count alternating permutations in the symmetric group. Springer defined a generalization of these numbers for each finite Coxeter group…
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 $y \in W$…
We show that for a large class $\mathcal{W}$ of Coxeter groups the following holds: Given a group $W_\Gamma$ in $\mathcal{W}$, the automorphism group ${\rm Aut}(W_\Gamma)$ virtually surjects onto some infinite Coxeter group. In particular,…
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…
Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erd\"os-R\'enyi model). In this paper, we extend this model to study random general Coxeter groups…
We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
We give explicit necessary and sufficient conditions for the abstract commensurability of certain families of 1-ended, hyperbolic groups, namely right-angled Coxeter groups defined by generalized theta-graphs and cycles of generalized…
We show that the (2,4,5) triangle Coxeter group is not systolic.
We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
Cactus groups are traditionally defined based on symmetric groups, and pure cactus groups are particular subgroups of cactus groups. Mostovoy showed that pure cactus groups embed into right-angled Coxeter groups. We generalize this result…
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 show that every Coxeter group that is not virtually abelian and for which all labels in the corresponding Coxeter graph are powers of 2 or infinity can be mapped onto uncountably many infinite 2-groups which, in addition, may be chosen…
In 2011, Barot and Marsh provided an explicit construction of presentation of a finite Weyl group $W$ by any quiver mutation-equivalent to an orientation of a Dynkin diagram with Weyl group $W$. The construction was extended by the authors…
In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In this paper, we show that the observed fractals are exactly the ball packings described by Boyd and…
We introduce a class of affine Deligne--Lusztig varieties that we call of positive Coxeter type. We show that the affine Deligne--Lusztig varieties of positive Coxeter type have a very simple and explicitly described geometric structure.…