Related papers: Complex hyperbolic and projective deformations of …

We study deformations of non-cocompact lattices of ${\rm SO}(n,1)$ into ${\rm SU}(n,1)$ and ${\rm SO}(n+1,1)$. A necessary condition for these deformations to remain discrete and faithful (when $n \geqslant 3$) is for the parabolic…

In this note, we study deformations of discrete and Zariski dense subgroups of SU(2, 1) in quaternionic hyperbolic space. Specifi- cally we consider two examples coming from representations of 3-manifold groups (the figure eight knot and…

We produce a complete list of group presentations for singly-cusped Bianchi groups, $PSL_2 (\mathcal{O}_d)$ where $\mathcal{O}_d$ is the ring of integers for $\mathbb{Q}(\sqrt{d})$ and $d$ is -1, -2, -3, -7, -11, -19, -43, -67, or -163. To…

In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…

We give formulae for the Chen-Ruan orbifold cohomology for the orbifolds given by a Bianchi group acting on complex hyperbolic 3-space. The Bianchi groups are the arithmetic groups PSL\_2(A), where A is the ring of integers in an imaginary…

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group…

Denote by Q(sqrt{-m}), with m a square-free positive integer, an imaginary quadratic number field, and by A its ring of integers. The Bianchi groups are the groups SL_2(A). We reveal a correspondence between the homological torsion of the…

Let $K$ be a $\mathbb{Q}$-Clifford algebra associated to an $(n-1)$-ary positive definite quadratic form and let $\mathcal{O}$ be a maximal order in $K$. A Clifford-Bianchi group is a group of the form $\operatorname{SL}_2(\mathcal{O})$…

We construct quantum deformation of Poincar\'e group using as a starting point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of $SU(2,2)$ as a real form of multiparametric…

In this article we provide simple and provable bounds on the size and shape of the locus of discrete subgroups of $\mathsf{PSL}(2,\mathbb{C})\cong \operatorname{Isom}^+(\mathbb{H}^3)$ which split as a free product of cyclic groups…

Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N=4, d=1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a…

We provide the first examples of strongly dense representations of a hyperbolic 3-manifold group into $SL(4,\mathbb{R})$ and $SU(3,1)$ i.e. representations where every pair of non-commuting elements has Zariski dense image. Our examples are…

In this article we characterize the complex hyperbolic groups that leave invariant a copy of the Veronese curve in $\Bbb{P}^2_{\Bbb{C}}$. As a corollary we get that every discrete compact surface group in $\PO^+(2,1)$ admits a deformation…

Farre, Pozzetti and Viaggi proved that any (d-k)-hyperconvex subgroup of PSL(d,C) is virtually isomorphic to a convex cocompact Kleinian group and that its k-th simple root critical exponent is at most 2. We show that a (d-k)-hyperconvex…

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…

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ be a $p$-divisible group over $k$ which is not isoclinic. Let $\scrD$ (resp. $\scrD_k$) be the formal deformation space of $D$ over $\Spf(W(k))$ (resp. over…

In this article we construct a type of deformations of representations $\pi_1(M)\rightarrow G$ where $G$ is an arbitrary lie group and $M$ is a large class of manifolds including CAT(0) manifolds. The deformations are defined based on…

Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of…

Let $X$ be a negatively curved symmetric space and $\Gamma$ a non-cocompact lattice in $\rm{Isom}(X)$. We show that small, parabolic-preserving deformations of $\Gamma$ into the isometry group of any negatively curved symmetric space…

We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is $SU(p,q)$ (resp. $SO^* (2n)$, $n$ odd) and the surface group is maximal in some…