Related papers: Most Hitchin representations are strongly dense

This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is…

Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly…

We study the S-integral points on the complement of a union of hyperplanes in projective space, where S is a finite set of places of a number field k. In the classical case where S consists of the set of archimedean places of k, we…

We survey the theory of Hitchin representations of Fuchsian groups and describe a conjectural geometric picture of an augmented Hitchin component.

Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles, allowing the Higgs field to be twisted by an arbitrary line bundle. We consider this generalization in the context of $G$-Higgs bundles for a real reductive Lie group…

In this article we prove that the co-compactness of the arithmetic lattices in a connected semisimple real Lie group is preserved if the lattices under consideration are representation equivalent. This is in the spirit of the question posed…

Using the work of Bonahon-Dreyer and Fock-Goncharov, one can construct a real-analytic parameterization for the PSL(n,R) Hitchin component of a surface S, that is explicitly analogous to the Fenchel-Nielsen coordinates on the Teichmuller…

Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed…

We introduce \emph{k-positive representations}, a large class of $\{1,\ldots,k\}$--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are…

We show that for all $k\geq 4$, $\varepsilon >0$, and $n$ sufficiently large, every $k$-uniform hypergraph on $n$ vertices in which each set of $k-3$ vertices is contained in at least $(5/8 + \varepsilon) \binom{n}{3}$ edges contains a…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

We prove that Sp(2d;R), HSp(2d) and pseudo unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non periodic dynamical systems. For Schr\"odinger operators on the strip, we prove a…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

We study the character variety of representations of the fundamental group of a closed surface of genus $g\geq2$ into the Lie group SO(n,n+1) using Higgs bundles. For each integer $0<d\leq n(2g-2),$ we show there is a smooth connected…

It is well known that the Tchebotarev density theorem implies that an irreducible $\ell$-adic representation $\rho$ of the absolute Galois group of a number field $K$ is determined (up to isomorphism) by the characteristic polynomials of…

We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as…

Recently Ivanov and Skvortsov introduced continuous Dyson-Maleev (DM) representations of supersymmetric non-linear sigma models and motivated that these representations are non-perturbatively exact. Basic to all continuous DM…

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a…

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 study reductive subgroups $H$ of a reductive linear algebraic group $G$ -- possibly non-connected -- such that $H$ contains a regular unipotent element of $G$. We show that under suitable hypotheses, such subgroups are $G$-irreducible in…