Related papers: Generic stabilisers for actions of reductive group…

This paper investigates the toral stabilizer of a finite-dimensional restricted Lie algebra $(\mathfrak{g},[p])$, defined over an algebraically closed field $k$ of positive characteristic. We compute the group of toral stabilizers of some…

The main result of this paper (Theorem B) asserts that under natural conditions, any weakly-split Tits system in G(k), G a reductive or quasi-reductive group over an arbitrary field k, is the standard one.

Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$, and $G$ is not metacyclic. Then $G$ always has a regular orbit on $V$ except for a few "small" cases. We completely…

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…

Let $G$ be a Lie group $G$ with representation $\rho$ on a real simple $G$-module $\mathbb{V}$. We will call the orbits of the induced action of $\rho$ on the projectivization $P\mathbb{V}$ the projective orbits, and projective orbits of…

We show that the local-global divisibility in commutative algebraic groups defined over number fields can be tested on sets of primes of arbitrary small density, i.e. stable and persistent sets. We also give a new description of the…

Let G be a transitive group of permutations of a finite set X, and suppose that some element of G has at most two orbits on X. We prove that any two maximal chains of groups between G and a point-stabilizer of G have the same length, and…

We prove that any ergodic measure-preserving action of an irreducible lattice in a semisimple group, with finite center and each simple factor having rank at least two, either has finite orbits or has finite stabilizers. The same dichotomy…

Let $k$ be a field, let $G$ be a reductive algebraic group over $k$, and let $V$ be a linear representation of $G$. Geometric invariant theory involves the study of the $k$-algebra of $G$-invariant polynomials on $V$, and the relation…

Let $G:=G_2(K)$ be a simple algebraic group of type $G_2$ defined over an algebraically closed field $K$ of characteristic $p>0$. Let $\sigma$ denote a standard Frobenius automorphism of $G$ such that $G_\sigma\cong G_2(q)$ with $q\geq 4$.…

Let $G$ be an affine algebraic group over an algrebraically closed field $\mathbb K$ of characteristic 0 and $H$ be a subgroup of $G$. The stabilizer of all the set of all vector-functions of $\mathbb K[G]^H$ with respect to the right…

We prove that any ergodic nonatomic probability-preserving action of an irreducible lattice in a semisimple group, at least one factor being connected and higher-rank, is essentially free. This generalizes the result of Stuck and Zimmer…

Let $G$ be a closed permutation group on a countably infinite set $\Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any probability…

We study definably compact definably connected groups definable in a sufficiently saturated real closed field $R$. We introduce the notion of group-generic point for $\bigvee$-definable groups and show the existence of group-generic points…

We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locally and we provide some evidence for this conjecture.…

In this paper we exhibit a minimal set of generators form the annihilator of even neat elements of the exterior algebra of a vector space, when the base field is of positive characteristic and thus we prove the conjecture we established in…

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if…

We study a relative variant of Serre's notion of $G$-complete reducibility for a reductive algebraic group $G$. We let $K$ be a reductive subgroup of $G$, and consider subgroups of $G$ which normalise the identity component $K^{\circ}$. We…