Related papers: Prehomogeneous tensor spaces

In this note, we prove that if $(G,V)$ is a prehomogeneous vector space over any field $k$ such that the stabilizer of a generic point is reductive, the set of semi-stable points is a single orbit over the separable closure of $k$.

The purpose of the paper is to prove an analogous correspondence for the above prehomogeneous vector space (1)-(3). For case (1) the correspondence is bijective. However, it turns out that the correspondence is not bijective for cases (2),…

We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techniques to determine, for any base global field $F$, the…

We consider the prehomogeneous vector space of pairs of ternary quadratic forms. For the lattice of pairs of integral ternary quadratic forms and its dual lattice, there are six zeta functions associated with the the prehomogeneous vector…

Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal…

Motivated by applications to duality theorems for $p$-adic pro-\'etale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full…

This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the \'etale modules…

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is…

Given an n-tuple of positive real numbers, Konno defines an algebraic variety called a hyperpolygon space, a hyperkahler analogue of the Kahler variety parametrizing spacial polygons with fixed edge lengths. The ordinary polygon space can…

In this paper we study the analytic properties of a multiple Dirichlet series associated to the prehomogeneous vector space of binary cubic forms.

It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general.…

In this article, we introduce inhomogeneous Sobolev spaces that naturally generalise the standard Sobolev-Slobodeckij spaces. The inhomogeneity of these spaces is governed by a set function $\mu$, referred to as an environment. In the case…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\rm SO}^{*}(2n){\rm Sp}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous…

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.…

Let $(\tilde Q,g) $ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),\omega^H \otimes \omega^E)$, we give an…

We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…

In the setting of spaces of homogeneous type, we study some Hardy type inequalities, which notably appeared in the proofs of local T(b) theorems as in [AR]. We give some suffi cient conditions ensuring their validity, related to the…

We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…

The first author with B. Sturmfels studied the variety of matrices with eigenvectors in a given linear subspace, called Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the…