Related papers: Classification of reflexibile regular Cayley maps …
We discuss the classification of reflection subgroups of finite and affine Weyl groups from the point of view of their root systems. A short case free proof is given of the well known classification of the isomorphism classes of reflection…
A graph is said to be a bi-Cayley graph over a group H if it admits H as a group of automorphisms acting semiregularly on its vertices with two orbits. A non-abelian group is called an inner-abelian group if all of its proper subgroups are…
We explicitly determine all CI-groups with respect to ternary relational structures that have the form $C \times D$, where $C$ is cyclic and $D$ is either a dicyclic group whose order is not divisible by $3$ or a dihedral group. Such groups…
In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.
We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (for a generic light position). We also give simple formulas…
A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Here we generalize that notion to maniplexes and polytopes. We define $\mathcal{M}$ to be a \emph{Cayley extension} of…
This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is…
The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate its group of automorphisms, its algebra of derivations and its gradings.
A Cayley digraph on a group $G$ is called NNN if the Cayley digraph is normal and its automorphism group contains a non-normal regular subgroup isomorphic to $G$. A group is called NNND-group or NNN-group if there is an NNN Cayley digraph…
In this paper, we construct some non-normal Cayley graphs and explicitly provide their spectra and eigenspaces using representation theory of finite groups.
A Cayley (di)graph $Cay(G,S)$ of a group $G$ with respect to $S$ is said to be normal if the right regular representation of $G$ is normal in the automorphism group of $Cay(G,S)$, and is called a CI-(di)graph if there is $\alpha\in Aut(G)$…
In this paper, we investigate the existence of fractional revival on semi-Cayley graphs over finite abelian groups. We give some necessary and sufficient conditions for semi-Cayley graphs over finite abelian groups admitting fractional…
In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the…
We give a classification of Lattes maps on P^2.
We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…
In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.
We give a geometric description of a certain class of epimorphisms between complex reflection groups. We classify these epimorphisms, which can be interpreted as ``morphisms'' between the diagrams symbolizing standard presentations by…
We introduce S-nondegenerate formal CR maps and establish their convergence (revision of a preliminary version).
We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.
Recently, several works by a number of authors have studied integrality, distance integrality, and distance powers of Cayley graphs over some finite groups, such as dicyclic groups and (generalized) dihedral groups. Our aim is to generalize…