Related papers: On totally hyperbolic non-Fuchsian type-preserving…

We prove the representation given by a stable $\alpha_1$-cyclic parabolic $\mathrm{SO}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is $\{\alpha_2\}$-almost dominated. This is a generalization of Filip's result on…

Let $F$ be a non-archimedean local field and $G={\bf{G}}(F)$ the group of $F$-rational points of a connected reductive $F$-group. Then we have the Langlands classification of complex irreducible admissible representations $\pi$ of $G$ in…

Hyperbolic homogeneous polynomials with real coefficients, i.e., hyperbolic real projective hypersurfaces, and their determinantal representations, play a key role in the emerging field of convex algebraic geometry. In this paper we…

In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy…

We show that Norbury's McShane identity for nonorientable cusped hyperbolic surfaces N generalizes to quasifuchsian representations of pi_1(N) as well as pseudo-Anosov mapping Klein bottles with singular fibers given by N.

Let $\Gamma$ denote the $d = 2$ Bianchi group $\operatorname{PSL}(2,\mathbb{Z}[\sqrt{-2}])$. We give an explicit description of all conjugacy classes of maximal nonelementary Fuchsian subgroups of $\Gamma$ as integral orders of certain…

Let $S$ be a surface of genus $g$ at least $2$. A representation $\rho:\pi_1S\longrightarrow \text{PSL}_2\Bbb R$ is said to be purely hyperbolic if its image consists only of hyperbolic elements other than the identity. We may wonder under…

We show that for every representation $ \rho : \pi_{1} (S_{g}) \to \text{Isom}(X) $ of the fundamental group of a genus $ g \ge 2 $ surface to the isometry group of a complete $ \text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian…

We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we…

Let $E/F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$, and $G$ be the unramified unitary group $U(2, 1)(E/F)$. For an irreducible smooth representation $\pi$ of $G$ over…

Let $\Sigma_g$ be a compact, connected, orientable surface of genus $g \geq 2$. We ask for a parametrization of the discrete, faithful, totally loxodromic representations in the deformation space ${\rm Hom}(\pi_1(\Sigma_g), {\rm…

In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle theory, the theory of Anosov representations, and…

We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in $\mathrm{SL}(2m+1,\mathbb{R})$. For $m=1$ our techniques allow to recover several known results for Hitchin…

We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is the fundamental group of the orbifold S^2(2,...,2) and thus contains a surface group…

We give explicit formulas on total Springer representations for classical types. We also describe the characters of restrictions of such representations to a maximal parabolic subgroup isomorphic to a symmetric group. As a result, we give…

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…

We give a new lower bound on the number of connected components of the space of representations of a surface group into the group of orientation preserving homeomorphisms of the circle. Precisely, for the fundamental group of a genus g…

Let $\pi $ be an irreducible smooth complex representation of a general linear $p$-adic group and let $\sigma $ be an irreducible complex supercuspidal representation of a classical $p$-adic group of a given type, so that $\pi\otimes\sigma…

In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…

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…