Related papers: Closed H-orbits in G-varieties

Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following property: for every vector v in V, the closure of its T-orbit is…

For a linear group $G$ acting on an absolutely irreducible variety $X$ over the rationals $\QQ$, we describe the orbits of $X(\QQ_p)$ under $G(\QQ_p)$ and of $X(\FF_p((t)))$ under $G(\FF_p((t)))$ for $p$ big enough. This allows us to show…

The excursion algebra associated to a scheme X over a finite field and a reductive group G is the algebra of global functions on the stack of arithmetic G-local systems on X. When X is a curve, this algebra acts on the space of automorphic…

The existence of invariant transversals for a normal subgroup $H$ in a group $G$ is investigated. This yields counterexamples to a conjecture in case $H$ is abelian and $G$ is finite.

In the present article we study the following problem. Let G be a linear algebraic group over Q, $\Gamma$ be an arithmetic lattice and H be an observable Q-subgroup. There is a H-invariant measure $\mu_H$ supported on the closed submanifold…

We introduce and study diamonds of GL(2,R)-invariant subvarieties of Abelian and quadratic differentials, which allow us to recover information on an invariant subvariety by simultaneously considering two degenerations, and which provide a…

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

Luna's etale slice theorem is a useful theorem for the local study of quotients by reductive algebraic groups. In this article, we show that the slice theorem can also be used to study local structures of invariant Hilbert schemes. By using…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable…

Let $ \tilde{G} $ be an algebraic group acting on a variety $ \tilde{L} $, and $ G \subset \tilde{G} $ a subgroup which leaves a subvariety $ L \subset \tilde{L} $ stable. For a $ G $-orbit $ O_G = G u (u \in L) $ in $ L $, we can associate…

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…

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…

Let $G$ be a connected, complex reductive Lie group and $G/H$ a spherical homogenous space. Let $(X,L)$ be a polarized $G$-variety which is a spherical embedding of $G/H$. In this paper we classify $G$-equivariant normal $\mathbb R$-test…

For a complex variety $\hat X$ with an action of a reductive group $\hat G$ and a geometric quotient $\pi: \hat X \to X$ by a closed normal subgroup $H \subset \hat G$, we show that open sets of $X$ admitting good quotients by $G=\hat G /…

We characterise the strictly closed left invariant C*-subalgebras of the C*-algebra C_b(G) of bounded continuous functions on a locally compact group G. On the dual side, we characterise the strictly closed invariant C*-subalgebras of the…

We prove that if $G\subset\text{Diff}^{1}(\mathbb{R}^2)$ is an Abelian subgroup generated by a family of commuting diffeomorphisms of the plane, all of which are $C^{1}$-close to the identity in the strong $C^{1}$-topology, and if there…

We present geometric realizations of horospherical two-orbit varieties, by showing that their blow-up along the unique closed-invariant orbit is the zero locus of a general section of a homogeneous vector bundle over some auxiliary variety.…