Related papers: On Reconstructing Configurations of Points in ${\m…
We present a complete algebraic description of the field of first-order joint projective invariants for configurations of \( n \) points in the plane, under the natural diagonal action of the projective group \( PGL(3,\mathbb{R}) \). For \(…
In this paper, we present a method for constructing point primitive block transitive $t$-designs invariant under finite groups. Furthermore, we demonstrate that every point and block primitive $G$-invariant design can be generated using…
One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…
We show that all permutations in $S_n$ can be generated by affine unicritical polynomials. We use the $\operatorname{PGL}$ group structure to compute the cycle structure of permutations with low Carlitz rank. The tree structure of the group…
We consider the action of the projective group $PGL(3,\mathbb{R})$ on the $n$-fold first-order jet space of point configurations on the plane. Using the method of moving frames, we construct an explicit complete generating set for the field…
For $q = p^n$ with $p$ an odd prime, the projective linear group $PGL(2,q)$ can be seen as the stabilizer of a conic $O$ in a projective plane $\pi = PG(2,q)$. In that setting, involutions of $PGL(2,q)$ correspond bijectively to points of…
It was suggested method of constructing of irreducible projective representations in different points of Brilluin zone. Points \Gamma, \Lambda, Z, S, A, \Sigma, M, V, R, and X of space symmetry groups $P4_{1}2_{1}2$ and $P4_{3}2_{1}2$ were…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
We give a classification of ordered five points in $\mathbb P^3$ under the diagonal action of $GL_4$ over an algebraically closed field of characteristic $0$, by an explicit description of the diagonal action of $GL_4$ on the quintuple of…
In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…
We rephrase the problem of 3D reconstruction from images in terms of intersections of projections of orbits of custom built Lie groups actions. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between ordinary and symbolic powers of ideals, in the theory of…
Three-dimensional N-extended superconformal symmetry is studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
We consider the ring of invariants of n points on the projective line. The space (P^1)^n // PGL_2 is perhaps the first nontrivial example of a Geometry Invariant Theory quotient. The construction depends on the weighting of the n points.…
The aim of this paper is to clear up the problem of the connection between the 3D geometric moments invariants and the invariant theory, considering a problem of describing of the 3D geometric moments invariants as a problem of the…
The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…