Related papers: Proper affine deformations of positive representat…

We classify tube domains in $\mathbb C^{n+1}$ ($n\ge 1$) with affinely homogeneous base of their boundary and a.) with positive definite Levi form and b.) with Lorentzian type Levi form and affine isotropy of dimension at least…

In this paper, we study a natural class of groups that act as affine transformations of $\mathbb T^N$. We investigate whether these solvable, "abelian-by-cyclic," groups can act smoothly and nonaffinely on $\mathbb T^N$ while remaining…

We study $\mathbb{R}^k \times \mathbb{Z}^\ell$ actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations. Such actions are called totally Cartan actions. We…

A Fock representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is constructed by three bosonic fields for an arbitrary level with the help of the Drinfeld realization.

In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…

We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic…

Among the remarkable properties shared with convex cocompact representations, Anosov representations admit cocompact domains of discontinuity in flag varieties. For representations produced by embedding Fuchsian representations into higher…

Let $BS(1,n)= <a,b : a b a ^{-1} = b ^n>$ be the solvable Baumslag-Solitar group, where $n \geq 2$. We study representations of $BS(1, n)$ by homeomorphisms of closed surfaces with (pseudo-)Anosov elements. That is, we consider a closed…

In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup of Aut(S) generated by all its algebraic subgroups is not generated by any countable family of such subgroups,…

We construct for each conformal structure on a closed orientable surface of genus at least 2 a proper slice in the character variety of representations of the associated surface group into SL(3,R) that belongs to the Barbot component and…

We list all finite abelian groups which act effectively on smooth cubic fourfolds.

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We try to understand the geometric properties of $n$-manifolds ($n\geq 2$) with geometric structures modeled on $(\bR P^n, \PGL(n+1, \bR))$, i.e., $n$-manifolds with projectively flat torsion free affine connections. We define the notion of…

Let $BS(1, n)=< a, b | aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ n\geq 2$. It is known that B(1, n) is isomorphic to the group generated by the two affine maps of the line : $f_0(x) = x + 1$ and $h_0(x) = nx $. The…

We show that the fundamental groups of all non-compact, arithmetic, hyperbolic, $n$-manifolds for $n\geq 4$ contain thin surface subgroups. As a consequence of the proof of this theorem we also show that the fundamental groups of the…

Let $M_\phi$ be a surface bundle over a circle with monodromy $\phi:S \rightarrow S$. We study deformations of certain reducible representations of $\pi_1(M_\phi)$ into $\text{SL}(n,\mathbb{C})$, obtained by composing a reducible…

We construct examples of normal affine varieties X of dimension greater than or equal to 4 such that the group of special automorphisms SAut(X) acts on X with an open orbit O and the complement X\O has codimension one.

Q-map spaces form an important class of quaternionic K\"ahler manifolds of negative scalar curvature. Their one-loop deformations are always inhomogeneous and have been used to construct cohomogeneity one quaternionic K\"ahler manifolds as…

We construct a polynomial family of semisimple left module categories over the representation category of the Drinfeld-Jimbo deformation, with the fusion rule of the representation category of each Levi subalgebra. In this construction we…