Related papers: Dominating surface-group representations into $\ma…

We define a condition called almost strict domination for pairs of representations $\rho_1:\pi_1(S_{g,n})\to \textrm{PSL}(2,\mathbb{R})$, $\rho_2:\pi_1(S_{g,n})\to G$, where $G$ is the isometry group of a Hadamard manifold $(X,\nu)$, and…

This paper deals with non-Archimedean representations of punctured surface groups in PGL(3), associated actions on Euclidean buildings (of type A2), and degenerations of real convex projective structures on surfaces. The main result is…

We characterize the monodromies of projective structures with fuchsian-type singularities. Namely, any representation from the fundamental group of a Riemann surface of finite-type in $PSL_2(\mathbb{C})$ can be represented as the holonomy…

In this note, we give an explicit counterexample to the simple loop conjecture for representations of surface groups into PSL(2,R). Specifically, we show that for any surface with negative Euler characteristic and genus at least 1, there…

We describe a family of representations of $\pi_1(\Sigma)$ in PU(2,1), where $\Sigma$ is a hyperbolic Riemann surface with at least one deleted point. This family is obtained by a bending process associated to an ideal triangulation of…

We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\rho$ of $\pi_1(S)$ such that if $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then…

The compact hyperbolic triangle group $\Delta(p,q,r)$ admits a canonical representation to $\mathrm{PSL}_2(\mathbf{R})$ with discrete image which is unique up to conjugation. The trace field of this representation is \[K =…

Let $\Gamma$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order of any non-trivial torsion element of $\Gamma$. Then…

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL(2,K) representation variety, where K is the field of real or complex numbers, answering a…

We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell…

We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $\SL(n,\R)$ that satisfy partial hyperconvexity properties inspired from Labourie's work. This is the case for several open sets of Anosov…

Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…

We carry out a detailed study of the structure of domains of discontinuity $\Omega_\rho$ in $\mathbb{RP}^3$ of $\text{PSL}_4(\mathbb{R})$-Hitchin representations $\rho$. We then prove the foliated component $\Omega_\rho^1$ of $\Omega_\rho$…

We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on…

Let $S$ be a closed surface of genus $g \geq 2$ and let $\rho$ be a maximal $\mathrm{PSL}(2, \mathbb{R}) \times \mathrm{PSL}(2, \mathbb{R})$ surface group representation. By a result of Schoen, there is a unique $\rho$-equivariant minimal…

The fundamental group of every surface that is not the projective plane or Klein bottle has a representation to a torsion-free group of upper-triangular matrices in SL(2,R) with no simple loop (i.e. a nontrivial element representing a…

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

In the paper "Pappus's theorem and the modular group", R. Schwartz constructed a 2-dimensional family of faithful representations $\rho_\Theta$ of the modular group $\mathrm{PSL}(2,\mathbb{Z})$ into the group $\mathscr{G}$ of projective…

In this paper we study the Fock representation of a certain $*$-algebra which appears naturally in the framework of quantum group theory. It is also a generalization of the twisted CCR-algebra introduced by W. Pusz and S.~Woronowicz. We…