Related papers: Maximal representations of uniform complex hyperbo…

A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…

We give a spinorial representation of a submanifold of any dimension and co-dimension in a symmetric space $G/H,$ where $G$ is a complex semi-simple Lie group and $H$ is a compact real form of $G.$ This in particular includes…

We are given a finite group $H$, an automorphism $\tau$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langle\sigma\rangle$ of order $r$, and an absolutely irreducible…

For an even, integral hyperbolic lattice $L$, the symmetry group of $L$ is the quotient of the group of isometries of $L$ by the Weyl subgroup of $(-2)$-reflections. Following Nikulin, the exceptional lattice of $L$ is defined as the…

Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…

Consider $n \geq 2$. In this paper we prove that the group $\text{PU}(n,1)$ is $1$-taut. This result concludes the study of $1$-tautness of rank-one Lie groups of non-compact type. Additionally the tautness property implies a classification…

We identify the finitely many arithmetic lattices $\Gamma$ in the orientation preserving isometry group of hyperbolic $3$-space $\mathbb{H}^3$ generated by an element of order $4$ and and element of order $p\geq 2$. Thus $\Gamma$ has a…

We define the notion of affine Anosov representations of word hyperbolic groups into the affine group $\mathsf{SO}^0(n+1,n)\ltimes\mathbb{R}^{2n+1}$. We then show that a representation $\rho$ of a word hyperbolic group is affine Anosov if…

We introduce a type of minimal surface in the pseudo-hyperbolic space $\mathbb{H}^{n,n}$ (with $n$ even) or $\mathbb{H}^{n+1,n-1}$ (with $n$ odd) associated to cyclic $\mathrm{SO}_0(n,n+1)$-Higg bundles. By establishing the infinitesimal…

Given an oriented immersed hypersurface in hyperbolic space $\mathbb{H}^{n+1}$, its Gauss map is defined with values in the space of oriented geodesics of $\mathbb{H}^{n+1}$, which is endowed with a natural para-K\"ahler structure. In this…

Let $Y=\Gamma\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support…

Given two algebraic groups $G$, $H$ over a field $k$, we investigate the representability of the functor of morphisms (of schemes) $\mathbf{Hom}(G,H)$ and the subfunctor of homomorphisms (of algebraic groups) $\mathbf{Hom}_{\rm gp}(G,H)$.…

Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko…

We classify the effective and transitive actions of a Lie group $G$ on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that $G$ is a closed, connected Lie subgroup of…

In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct…

We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $\mathrm{PO}(n,1)$ with $n>3$. We further show that under an additional assumption (satisfied in all known cases), the covolumes of these…

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…

We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of SL(2,$\mathbb{H}$). So after having related the 16-dim Dirac…

We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of…

We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy…