Related papers: Proper affine actions: a sufficient criterion

Let G/H be a strongly regular homogeneous space such that H is a Lie group of inner type. We show that G/H admits a proper action of a discrete non-virtually abelian subgroup of G if and only if G/H admits a proper action of a subgroup L of…

We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g of…

We give a new and independent parameterization of the set of discrete series characters of an affine Hecke algebra $\mathcal{H}_{\mathbf{v}}$, in terms of a canonically defined basis $\mathcal{B}_{gm}$ of a certain lattice of virtual…

Let $(\pi, \mathcal H)$ be a continuous unitary representation of the (infinite dimensional) Lie group $G$ and $\gamma \: \mathbb R \to \mathrm{Aut}(G)$ define a continuous action of $\mathbb R$ on $G$. Suppose that $\pi^\#(g,t) = \pi(g)…

The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…

We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial…

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and f is a non-trivial irreducible…

In this article, we construct affine group schemes $GL(X)$ where $X$ is any object in the Verlinde category in characteristic $p$ and classify their irreducible representations. We begin by showing that for a simple object $X$ of…

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily…

Let $X$ be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group $G$. In this paper we provide sufficient conditions, formulated in terms of weight combinatorics, for the…

Let G be complex linear-algebraic group, H a subgroup, which is dense in G in the Zariski-topology. Assume that G/[G,G] is reductive and furthermore that (1) G is solvable, or (2) the semisimple elements in G'=[G,G] are dense. Then every…

We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.

Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This…

Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of…

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as…

Given a finitely generated group $G$, the possible actions of $G$ on the real line (without global fixed points), considered up to semi-conjugacy, can be encoded by the space of orbits of a flow on a compact space $(Y, \Phi)$ naturally…

In this article we establish the arithmetic purity of strong approximation for certain semi-simple simply connected $k$-simple linear algebraic groups and their homogeneous spaces over a number field $k$. For instance, for any such group…

Let $N$ be a manifold of dimension $m$ with a flat vector bundle given by a representation $\rho:\pi_1(N) \rightarrow \mathrm{GL}(n, \mathbf{R})$ where $\pi_1(N)$ is finitely generated. The holonomy group $\rho$ is a $k$-partially…

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…

We will first clarify the loop group formulations for both hyperbolic and elliptic definite affine spheres in R^3. Then we classify the rational elements with 3 poles or 6 poles in a real twisted loop group, and compute dressing actions of…