Related papers: The CR structure of minimal orbits in complex flag…

We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we…

We define a CR structure on a distinguished hyperplane in $\mathbb{C}^{n+1}$ and the CR sub-Laplacian on this CR manifold. We also define symmetries of the CR sub-Laplacian in general and for this special case construct all of them using…

In this paper, we consider local holomorphic mappings f: M\to M' between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search…

Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a…

Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have…

We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of…

In this companion paper to our article {\em Accidental CR structures} (arxiv.org, January 2023), thought of as an appendix not submitted for publication, we provide complete explicit lists of infinitesimal CR automorphisms for the concerned…

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic…

In this paper, we study geometry of totally real minimal surfaces in the complex hyperquadric $Q_{N-2}$, and obtain some characterizations of the harmonic sequence generated by these minimal immersions. For totally real flat surfaces that…

For a non-compact simple Lie algebra $\mathfrak{g}$ over $\mathbb{R}$, we denote by $\mathcal{O}^{\mathbb{C}}_{\min,\mathfrak{g}}$ the unique complex nilpotent orbit in $\mathfrak{g} \otimes_\mathbb{R} \mathbb{C}$ containing all minimal…

In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of generalized flag manifolds. We prove that all these left-invariant geodesic orbit metrics…

We consider a group $G$ acting on a local dendrite $X$ (in particular on a graph). We give a full characterization of minimal sets of $G$ by showing that any minimal set $M$ of $G$ (whenever $X$ is different from a dendrite) is either a…

We classify the GL_p x GL_q-orbits in the flag variety for GL_{p+q} with rationally smooth closure, showing that they are all either already closed or are pullbacks from orbits with smooth closure in a partial flag variety.

Let $G/P$ be a rational homogeneous space (not necessarily irreducible) and $x_0\in G/P$ be the point at which the isotropy group is $P$. The $G$-translates of the orbit $Qx_0$ of a parabolic subgroup $Q\subsetneq G$ such that $P\cap Q$ is…

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit…

Let $G$ be a complex reductive group and $P$ be a parabolic subgroup of $G$. In this paper the authors address questions involving the realization of the $G$-module of the global sections of the (twisted) cotangent bundle over the flag…

A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup…