Related papers: Horospherical subgroups in positive characteristic

We determine which tangential varieties of homogeneously embedded rational homogeneous varieties are spherical. We determine the homogeneous coordinate rings and rings of covariants of the tangential varieties of homogenously embedded…

We introduce the classes of (strongly) ($\Theta$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces.…

We show that smooth projective horospherical varieties with nef tangent bundles are rational homogeneous spaces.

Let $X=G/H$ be a spherical variety over an algebraically closed field of characteristic $p\ge0$. We compute the $p'$-parts of $\pi_0(H)$ and $\pi_1(X)$ from the spherical system of $X$.

We classify spherical conjugacy classes in a simple algebraic group over an algebraically closed field of good, odd characteristic.

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the…

Polar weighted homogeneous polynomials are the class of special polynomials of real variables $x_i,y_i, i=1,..., n$ with $z_i=x_i+\sqrt{-1} y_i$, which enjoys a "polar action". In many aspects, their behavior looks like that of complex…

We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…

We define the Z/2Z Hodge spaces H_{pq}(\Sigma) of a fan \Sigma. If \Sigma is the normal fan of a reflexive polytope \Delta then we use polyhedral duality to compute the Z/2Z Hodge Spaces of \Sigma. In particular, if the cones of dimension…

Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems. Whenever nonempty, all such complete…

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.…

The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. We classify affine homogeneous spaces G/H of complexity one. These…

We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its…

We investigate in detail a homomorphism which we call the 2-Selmer signature map from the $2$-Selmer group of a number field $K$ to a nondegenerate symmetric space, in particular proving the image is a maximal totally isotropic subspace.…

We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.

This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map…

We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from a sphere to an orthogonal or a unitary group is homotopic…

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

We study the homogeneous ind-spaces $\mathrm{GL}(\mathbf{s})/\mathbf{P}$ where $\mathrm{GL}(\mathbf{s})$ is a strict diagonal ind-group defined by a supernatural number $\mathbf{s}$ and $\mathbf{P}$ is a parabolic ind-subgroup of…

We prove local existence of complex-valued harmonic morphisms from any Riemannian homogeneous spaces of positive curvature, except the Berger space Sp(2)/SU(2).