Related papers: Classification of real and complex 3-qutrit states

We consider in this paper the $FRS$-deformations of a family of space curves with codimension $\leq 3$. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.

We classify the real and strongly real conjugacy classes in $GL_n(q)$, $SL_n(q)$, $PGL_n(q)$, $PSL_n(q)$, and all quasi-simple covers of $PSL_n(q)$. In each case we give a formula for the number of real, and the number of strongly real,…

We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…

We numerically study orders of planer type $(xy,x^2-y^2)$ quadrupoles on a triangular lattice with nearest-neighbor isotropic $J$ and anisotropic $K$ interactions. This type of quadrupoles possesses unique single-ion anisotropy proportional…

In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the…

This article gives a description of the diagonal $GL_3$-orbits on the quadruple projective variety $(\mathbb P^2)^4$. We give explicit representatives of orbits, and describe the closure relations of orbits. A distinguished feature of our…

In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line…

The general linear group GL(n, K) over a field K contains a particularly prominent subgroup U(n, K), consisting of all the upper triangular unipotent elements. In this paper we are interested in the case when K is the finite field F_q, and…

Let $H$ be a connected spherical subgroup of a semisimple algebraic group $G$. In this paper, we give a criterion for $H$-orbit closures in the flag variety of $G$ to have nice geometric and cohomological properties. Our main tool is the…

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, $\E$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries: the…

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…

We introduce the representation category $\mathscr{C}({\bf G})$ for a connected reductive algebraic group ${\bf G}$ which is defined over a finite field $\mathbb{F}_q$ of $q$ elements. We show that this category has many good properties for…

Let $F$ be any non-Archimedean local field with residue field of cardinality $q_F$. In this article, we obtain a classification of typical representations for the Bernstein components associated to the inertial classes of the form $[{\rm…

We determine the mean number of 3-torsion elements in the class groups of quadratic orders, where the quadratic orders are ordered by their absolute discriminants. Moreover, for a quadratic order $\mathcal{O}$ we distinguish between the two…

For a group $G$, let $\mathcal{F}_{n}$ be the family of all the subgroups of $G$ containing a subgroup isomorphic to $\mathbb{Z}^{r}$ for some $r=0,1,2,\dots ,n$ of finite index. Joecken, Lafont and S\'anchez Salda\~na computed the…

Let $F$ be a non-Archimedean local field and let $\mathcal{O}_{F}$ be its ring of integers. The orbit of an irreducible representation $\rho$ of $\mathrm{GL}_n(\mathcal{O}_F)$ is a conjugacy class in $\mathfrak{gl}_n(\mathcal{O}_F)$…

We obtain criteria for the class number of certain Richaud-Degert type real quadratic fields to be 3. We also treat a couple of families of real quadratic fields of Richaud-Degert type that were not considered earlier, and obtain similar…

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

We present an explicit description of the 'fine group gradings' (i.e. group gradings which cannot be further refined) of the real forms of the semisimple Lie algebras $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$. All together 12 real Lie algebras…

A query, about the orbit $P{\cal W}$ in real 3-space of a point $P$ under an isometry group ${\cal W}$ generated by edge rotations of a tetrahedron, leads to contrasting notions, ${\cal W}$ versus ${\cal S}$, of "rotation group". The set R…