Related papers: Irreducibly acting subgroups of $Gl(n,\rr)$

If the holonomy representation of an $(n+2)$--dimensional simply-connected Lorentzian manifold $(M,h)$ admits a degenerate invariant subspace its holonomy group is contained in the parabolic group $(\mathbb{R} \times SO(n))\ltimes…

We investigate left-invariant ${\rm G}_2^*$-structures on 7-dimensional Lie groups, focusing on those whose holonomy algebras are indecomposable and of type III, the latter meaning that the socle of the holonomy representation is maximal.…

Let $G$ be a finite group and let $k$ be an algebraically closed field of characteristic $2$ and let $M$ be an indecomposable $kG$-module which affords a non-degenerate $G$-invariant symmetric bilinear form. We introduce the symmetric…

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable…

This article is a report on the status of the problem of classifying the irriducibly acting subgroups of GL(n,R) that can appear as the holonomy of a torsion-free affine connection. In particular, it contains an account of the completion of…

Let G be a simple classical algebraic group over an algebraically closed field K of characteristic $p \ge 0$ with natural module W. Let H be a closed subgroup of G and let V be a nontrivial p-restricted irreducible tensor indecomposable…

Suppose that a group $G$ acts non-elementarily on a hyperbolic space $S$ and does not fix any point of $\partial S$. A subgroup $H\le G$ is said to be geometrically dense in $G$ if the limit sets of $H$ and $G$ coincide and $H$ does not fix…

We consider conformal actions of solvable Lie groups on closed Lorentzian manifolds. With anterior results in which we addressed similar questions for semi-simple Lie group actions, this work contributes to the understanding of the identity…

Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose also that $G$ is a classical group with natural module…

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear…

We develop Hodge theory for a Riemannian manifold $(M,g)$ with a background closed 3-form, H. Precisely, we prove that if the metric connections with torsion $\pm H$ have holonomy groups $G_\pm$, then the $d^H$-Laplacian preserves the…

We present a closed formula, analogous to the Weyl dimension formula, for the signature of an invariant Hermitian form on any finite-dimensional irreducible representation of a real reductive Lie group, assuming that such a form exists. The…

In this third part, we make the following hypothesis: representation $R=R(\alpha,\beta,\gamma ;l)$ of $W(p,q,r)$ is reducible and there exist a $G$-invariant non-nulle bilinear form where $G=Im R$. With those conditions, we know the…

This paper is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group $G$ is…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More…

Let A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a…

We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple…

Answering a question of J. Rosenberg, we construct the first examples of infinite characters on $GL_n(\mathbf{K})$ for a global field $\mathbf{K}$ and $n\geq 2.$ The case $n=2$ is deduced from the following more general result. Let $G$ a…

We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern--Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all…