Related papers: A remark on descent for Coxeter groups

Let T be a compact torus and X a nice compact T-space (say a manifold or variety). We introduce a functor assigning to X a "GKM-sheaf" F_X over a "GKM-hypergraph" G_X. Under the condition that X is equivariantly formal, the ring of global…

We determine the epimorphisms $A \to W$ from the Artin group $A$ of type $\Gamma$ onto the Coxeter group $W$ of type $\Gamma$, in case $\Gamma$ is an irreducible Coxeter graph of spherical type, and we prove that the kernel of the standard…

We develop a sheaf cohomology theory of algebraic varieties over an algebraically closed non-trivially valued non-archimedean field $K$ based on Hrushovski-Loeser's stable completion. In parallel, we develop a sheaf cohomology of definable…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

For an extension $1\rightarrow N \rightarrow \Gamma \xrightarrow{q} \Gamma / N \rightarrow 1$ of discrete countable groups, it is known that the Baum-Connes conjecture with coefficients holds for $\Gamma$ if it holds for $\Gamma / N$ and…

We present several new examples of reflection principles which apply to both class groups of number fields and picard groups of of curves over $\mathbb{P}^{1}/\mathbb{F}_{p}$. This proves a conjecture of Lemmermeyer about equality of 2-rank…

Let $\Gamma$ be a finitely presented group and $G$ a linear algebraic group over $\mathbb{R}$. A representation $\rho:\Gamma\rightarrow G(\mathbb{R})$ can be seen as an $\mathbb{R}$-point of the representation variety $\mathfrak{R}(\Gamma,…

A theorem of Tits - Vinberg allows to build an action of a Coxeter group $\Gamma$ on a properly convex open set $\Omega$ of the real projective space, thanks to the data $P$ of a polytope and reflection across its facets. We give sufficient…

Let $G$ be a reflection group acting on a vector space $V$ and let $\gamma$ be an automorphism of $V$ normalising $G$. We study how $\gamma$ acts on invariants and covariants (for various representations) of $G$, and properties of its…

In this article, we study the decomposition into irreducible components of the fixed point locus under the action of $\Gamma$ a finite subgroup of $\mathrm{SL}_2(\mathbb{C})$ of the smooth Nakajima quiver variety of the Jordan quiver. The…

We study strongly graded groupoids, which are topological groupoids $\mathcal G$ equipped with a continuous, surjective functor $\kappa: \mathcal G \to \Gamma$, to a discrete group $\Gamma$, such that $\kappa^{-1}(\gamma)\kappa^{-1}(\delta)…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \Gamma generated by r elements, we consider the representation spaces Hom(\Gamma,G) and Hom(\Gamma,K) with the natural…

We are interested in the McKay quiver $\Gamma(G)$ and skew group rings $A*G$, where $G$ is a finite subgroup of $\mathrm{GL}(V)$, where $V$ is a finite dimensional vector space over a field $K$, and $A$ is a $K-G$-algebra. These skew group…

If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-${\mathbb{Z}}$-module ${\mathcal{D}}_A(W)$ of the group algebra ${\mathbb{Z}} W$. We provide examples where this submodule is a subalgebra. This…

We prove that if $M \longrightarrow P$ is a small cover of a compact right-angled hyperbolic polyhedron $P$ then $M$ admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if $\pi_1(M)$ is commensurable…

Let $\Gamma$ be a $T$-ideal of identities of an affine PI-algebra over an algebraically closed field $F$ of characteristic zero. Consider the family $\mathcal{M}_{\Gamma}$ of finite dimensional algebras $\Sigma$ with $Id(\Sigma) = \Gamma$.…

(Makes a Gamma-acylic coherent resolution of a coherent sheaf on a projection scheme.)

Let $\mathbb{G}$ be a connected reductive group over $\mathcal{O}$, a complete discrete valuation ring with finite residue field $\mathbb{F}_q$. Let $R_{T_r,U_r}^{\theta}$ be a level $r$ Deligne--Lusztig representation of…

We consider a finite acyclic quiver $\mathcal{Q}$ and a quasi-Frobenius ring $R$. We endow the category of quiver representations over $R$ with a model structure, whose homotopy category is equivalent to the stable category of…