Related papers: On orbit closures of Borel subgroups in spherical …

Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous…

Let G be a reductive algebraic group over the complex number filed, and K = G^{\theta} be the fixed points of an involutive automorphism \theta of G so that (G, K) is a symmetric pair. We take parabolic subgroups P and Q of G and K…

Let $P$ be a parabolic subgroup in $SL_n(\mathbb C)$. We show that there is a $SL_n(\mathbb C)$-stable closed subvariety of an affine Schubert variety in an infinite dimensional partial Flag variety (associated to the Kac-Moody group…

We prove a relation between the $\bar\partial_M$ cohomology of a minimal orbit $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a flag manifold $G/Q$ and the Dolbeault cohomology of the Matsuki dual open orbit $X$ of the…

This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for…

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in…

The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then…

Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space…

Given a complex simply connected simple algebraic group $G$ of exceptional type and a maximal parabolic subgroup $P \subset G$, we classify all triples $(G,P,H)$ such that $H \subset G$ is a maximal reductive subgroup acting spherically on…

Let $G$ be a connected reductive algebraic group and $B$ be a Borel subgroup defined over an algebraically closed field of characteristic $p>0$. In this paper, the authors study the existence of generic $G$-cohomology and its stability with…

Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is called spherical provided it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Kr\"amer in 1979. In…

Let k be an algebraically closed field of characteristic p>0 and let G be a connected reductive group over k. Let B be a Borel subgroup of G and let g and b be the Lie algebras of G and B. Denote the first Frobenius kernels of G and B by…

We study equivalence relations $\mathcal R(\Gamma\curvearrowright G)$ that arise from left translation actions of countable groups on their profinite completions. Under the assumption that the action $\Gamma\curvearrowright G$ is free and…

Let $G$ be a classical group defined over the complex numbers with a Borel subgroup $B$. Choose a holomorphic involution of $G$ and let $K$ be its set of fixed points. The group $K$ acts on the flag variety $G/B$ with finitely many orbits…

For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate…

Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler…

Motivated by branching problems for principal series representations of the Lie group $G = GL(n,\mathbb R)$, we consider all pairs $(G', P)$ with $G'$ being the Levy factor of a parabolic subgroup of $G$ and $P$ a parabolic subgroup of $G$…

Let $G$ be a complex simply-connected semisimple Lie group and let $\frak{g}= Lie G$. Let $\frak{g} = \frak{n}_- +\frak{h} + \frak{n}$ be a triangular decomposition of $\frak{g}$. One readily has that $Cent\,U({\frak n})$ is isomorphic to…

Let $G=GL(n)$ be the $n\times n$ complex general linear group and let $\mathcal{B}_{n}$ be its flag variety. The standard Borel subgroup $B$ of upper triangular matrices acts on the product $\mathcal{B}_{n}\times \mathbb{P}^{n-1}$ with…

We study open orbits of symmetric subgroups of a simple connected Lie group G on a causal flag manifold. First we show that a flag manifold M of G carries an invariant causal structure if and only if G is hermitian of tube type and M is the…