Related papers: Odometer actions of the Heisenberg group

Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's…

We consider the family of $3 \times 3$ operator matrices ${\bf H}(K),$ $K \in {\Bbb T}^3:=(-\pi; \pi]^3$ associated with the lattice systems describing two identical bosons and one particle, another nature in interactions, without…

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in…

This paper gives a representation-theoretic interpretation of the Lerch zeta function and related Lerch $L$-functions twisted by Dirichlet characters. These functions are associated to a four-dimensional solvable real Lie group $H^{J}$,…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

We consider finitely generated group endowed with a word metric. The group acts on itself by isometries, which induces an action on its horofunction boundary. The conjecture is that nilpotent groups act trivially on their reduced boundary.…

We consider the biharmonicity condition for maps between Riemannian manifolds (see [BK]), and study the non-geodesic biharmonic curves in the Heisenberg group H_3. First we prove that all of them are helices, and then we obtain explicitly…

We study two sorts of actions on the space of conjugacy classes of irreducible $SU_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $SU_2$ and the other is the action by the outer…

Let $H = \mathrm{SO}(n,1)$ and $A = \{a(t): t \in \mathbb{R}\}$ be a maximal $\mathbb{R}$-split Cartan subgroup of $H$. Let $\Gamma \subset H \times H$ be a nonuniform lattice in $H \times H$ and $X_{\Gamma} : = H \times H/ \Gamma$. Let…

In this article we will see some properties that guarantee that a product of an ergodic non-singular action and a probability preserving ergodic action is also an ergodic action. We will start by proving 'The multiplier theorem' for locally…

The group E(3)=SO(3) *s T(3), that is the homogeneous subgroup of the Galilei group parameterized by rotation angles and velocities, defines the continuous group of transformations between the frames of inertial particles in Newtonian…

Let $T$ be a bounded linear operator on a Banach space $X$ satisfying $\|T^n\|/n \to 0$. We prove that $T$ is uniformly ergodic if and only if the one-sided ergodic Hilbert transform $H_Tx:= \lim_{n\to\infty} \sum_{k=1}^n k^{-1}T^k x$…

The paper is devoted to the large scale geometry of the Heisenberg group $\mathbb H$ equipped with left-invariant Riemannian distances. We prove that two such distances have bounded difference if and only if they are asymptotic, i.e., their…

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…

We consider the problems of measurable isomorphisms and joinings, measurable centralizers and quotients for certain classes of ergodic group actions on infinite measure spaces. Our main focus is on systems of algebraic origin: actions of…

Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus-$g$ surface with one boundary component, over non-commutative local systems…

We study the biholomorphic action of the Heisenberg group $\mathbb{H}_n$ on the Siegel domain $D_{n+1}$ ($n \geq 1$). Such $\mathbb{H}_n$-action allows us to obtain decompositions of both $D_{n+1}$ and the weighted Bergman spaces…

This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute the characters of all these representations…

For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurrent measured laminations. In particular, given a…

Let $G=\prod_{i=1}^{r} G_i$ be a product of simple real algebraic groups of rank one and $\Gamma$ an Anosov subgroup of $G$ with respect to a minimal parabolic subgroup. For each $v$ in the interior of a positive Weyl chamber, let $\mathcal…