Related papers: On the Hurwitz action in affine Coxeter groups

Let G be a compact group. Let (X,G) be a standard Borel G-measure space. We show that the group action on (X, G) is transitive if and only if it is ergodic. Using this result, we show that every irreducible covariant representation of a…

Let $W$ be a Coxeter group and $r\in W$ a reflection. If the group of order 2 generated by $r$ is the intersection of all the maximal finite subgroups of $W$ that contain it, then any isomorphism from $W$ to a Coxeter group $W'$ must take…

In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also…

We characterize the hypocompact radical of a semicrossed product in terms of properties of the dynamical system. We show that an element A of a semicrossed product is in the hypocompact radical if and only if the Fourier coefficients of A…

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 note we revisit Moussong's Characterization of Gromov-hyperbolic Coxeter groups. A Coxeter group is Gromov-hyperbolic if and only if it does not contain a subgroup isomorphic to $\mathbb{Z}^2$ which can be read off directly from the…

We describe a higher dimensional analogue of the Stallings folding sequence for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups which act properly co-compactly on…

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful…

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.

Let $\Gamma^+$ be the positive cone in a totally ordered abelian group $\Gamma$, and let $\alpha$ be an action of $\Gamma^+$ by endomorphisms of a $C^*$-algebra $A$. We consider a new kind of crossed-product $C^*$-algebra…

Let $\E$ be a finite dimensional Hilbert space. This note finds all factorizations of the right shift semigroup $\S^\E=(S_t^\E)_{t\ge 0}$ on $L^2(\R_+,\E)$ into the product of $n$ commuting contractive semigroups, i.e., characterizes all…

It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (respectively, any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that…

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well.…

Let $f: X\to X$ be a surjective endomorphism of a projective variety of dimension $d$. The aim of this paper is to study the action of $f$ on the numerical group of divisors. For exmaple, I proved that $f$ is cohomologically hyperbolic if…

In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let $(W,S)$ be a Coxeter system and let $T$ be a subset of $S$ such that the parabolic subgroup $W_T$ is infinite. Then we show that if a certain set is…

The Demazure product, also called the 0-Hecke product, is an associative operation on Coxeter groups with interesting properties and applications. In (Li et al 2024) it was shown that the Demazure product of two permutations can be…

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with…

Through highly non-constructive methods, works by Bestvina, Culler, Feighn, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a virtually solvable subgroup, then the space of its discrete…

We study actions by higher-rank abelian groups on quotients of semisimple Lie groups with finite center. First, we consider actions arising from the flows of two commuting elements of the Lie algebra--one nilpotent, and the other…

We report here the electrical transport and magnetic properties of the newly synthesized quaternary Heusler compound CoFeTiSn and CoFeVGa. We observe a striking change in the electronic transport properties of CoFeTiSn as the system…