Related papers: Polar spaces and embeddings of classical groups

A finite group G is called admissible over a given field if there exists a central division algebra that contains a G-Galois field extension as a maximal subfield. We give a definition of embedding problems of division algebras that extends…

In a noncompact harmonic manifold $M$ we establish finite dimensionality of the eigenspaces $V_{\lambda}$ generated by radial eigenfunctions of the form $\cosh r + c$. As a consequence, for such harmonic manifolds, we give an isometric…

We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…

Let $V$ be a finite-dimensional vector space over the field with $p$ elements, where $p$ is a prime number. Given arbitrary $\alpha,\beta\in \mathrm{GL}(V)$, we consider the semidirect products $V\rtimes\langle \alpha\rangle$ and…

In this paper we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the H\"ormander condition, and their corresponding sub-Laplacian. Embedding…

Flat surfaces that correspond to meromorphic $1$-forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify groups that appear as Veech groups of translation surfaces…

In this paper, we classify the $m$-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive…

It is shown that a topological group G is topologically isomorphic to the isometry group of a (complete) metric space iff G coincides with its G-delta-closure in the Rajkov completion of G (resp. if G is Rajkov-complete). It is also shown…

We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…

A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\mu$ defined on $V.$ Hence it can be regarded…

We classify all pairs $(V,H)$, where $H$ is a proper subgroup of $G=Sp_6(q)$, $q$ even, and $V$ is an $\ell$-modular representation of $G$ for $\ell\neq 2$ which is absolutely irreducible as a representation of $H$. This problem is…

Weakly-irreducible not irreducible subalgebras of $\so(1,n+1)$ were classified by L. Berard Bergery and A. Ikemakhen. In the present paper a geometrical proof of this result is given. Transitively acting isometry groups of Lobachevskian…

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra…

Let $F$ be a non-Archimedean local field with finite residue field. Let $\mathcal{A}^{et}_n(F)$ be the collection of isomorphism classes of essentially tame irreducible supercuspidal representations of $\mathrm{GL}_n(F)$ studied by…

We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this…

At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…

We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…

The Killing equation for a general Finsler space is set up. It is showed that the Killing equation of $(\alpha,\beta)$ space can be divided into two parts. One is the same with Killing equation of a Riemannian metric, another equation can…

Motivated by the recent works [Huan Yu, Quansen Jiu, and Dongsheng Li, 2021] and [Yanping Chen and Zihua Guo, 2021], we study the following extension of Calder\'on-Zygmund type singular integrals $$ T_{\beta}f (x) = p.v. \int_{\mathbb{R}^n}…

Given an imaginary quadratic extension $K$ of $\mathbb Q$, we classify the maximal nonelementary subgroups of the Picard modular group $\operatorname{PU}(1,2;\mathcal O_K)$ preserving a totally real totally geodesic plane in the complex…