Related papers: Subspaces of a para-quaternionic Hermitian vector …

Let E be a Real or Quaternionic Hermitian vector bundle over a Klein surface M. We study the action of the gauge group of E on the space of Galois-invariant unitary connections and we show that the closure of a semi-stable orbit contains a…

In the framework of the study of the $Sp(n)$-orbits in the real Grassmannian $G^\R(k,4n)$ of $k$-dimensional non oriented subspaces of a real $4n$-dimensional vector space $V$, here we consider the case of the isoclinic subspaces whose set…

We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…

In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

We show that an equivariantly embedded Hermitian symmetric space in a projective space, which contains neither a projective space nor a hyperquadric as a component, is characterized by their fundamental forms as a local submanifold of the…

Let $G$ be a finitely generated Kleinian group and let $\Delta$ be an invariant collection of components in its region of discontinuity. The Teichm\"uller space $T(\Delta,G)$ supported in $\Delta$, is the space of equivalence classes of…

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…

This article studies left-invariant Hermitian structures on Lie groups with two-dimensional commutator subgroups. We provide an explicit classification for two specific types of such structures, which we designate as Type I and Type II.…

Let $V$ be a finite dimensional vector space equipped with a non-degenerate Hermitian form over a field $\mathbb{K}$. Let $\mathcal{G}(V)$ be the graph with vertex set the $1$-dimensional non-degenerate subspaces of $V$ and adjacency…

Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4,…

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on a…

We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected…

We introduce a generalization of variations of Hodge structures living over moduli spaces of non-commutative deformations of complex manifolds. Hodge structure associated with a point of such moduli space is an element of Sato type…

This paper examines 8-dimensional Riemannian manifolds whose structure group reduces to ${SO(4)}_{ir}\subset GL(8,\mathbb R)$, the image of an irreducible representation of $SO(4)$ on $\mathbb R^8$. We demonstrate that such a reduction can…

Given a discrete subgroup $\Gamma$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $\Sigma$ of the (extended) hyperbolic plane by $\Gamma$. If $\Gamma$ contains an…

Parabosonic $P_{B}^{(n)}$ and parafermionic $P_{F}^{(n)}$ algebras are described as quotients of the tensor algebras of suitably choosen vector spaces. Their (super-) Lie algebraic structure and consequently their (super-) Hopf structure is…

Let $V$ be a vector space of dimension $N$ over the finite field $\mathbb{F}_q$ and $T$ be a linear operator on $V$. Given an integer $m$ that divides $N$, an $m$-dimensional subspace $W$ of $V$ is $T$-splitting if $V=W\oplus TW\oplus…