Related papers: Full Spark Frames in the Orbit of a Representation
We classify all spherical 2-designs that arise as orbits of finite group actions on real inner product spaces. Although it is well known that such designs can occur in representations without trivial components, we give a complete…
We construct a new infinite family of 4-dimensional isolated symplectic singularities with trivial local fundamental group, answering a question of Beauville raised in 2000. Three constructions are presented for this family: (1) as…
This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also…
We construct a new family of Cayley automatic representations of semidirect products $\mathbb{Z}^n \rtimes_A \mathbb{Z}$ for which none of the projections of the normal subgroup $\mathbb{Z}^n$ onto each of its cyclic components is finite…
A characterization is completed for finite groups acting arc-transitively on maps with square-free Euler characteristic, associated with infinite families of regular maps of square-free Euler characteristic presented. This is based on a…
We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary…
We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double of the group ring kG, we show that the self-extension…
We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
In this paper, we study skew frame starters, which are strong frame starters that satisfy an additional "skew" property. We prove three new non-existence results for cyclic skew frame starters of certain types. We also construct several…
We show the full structure of the frame set for the Gabor system $\mathcal{G}(g;\alpha,\beta):=\{e^{-2\pi i m\beta\cdot}g(\cdot-n\alpha):m,n\in\Bbb Z\}$ with the window being the Haar function $g=-\chi_{[-1/2,0)}+\chi_{[0,1/2)}$. The…
We apply a reduction to the Beauville systems to obtain a family of new algebraic completely integrable systems, related to curves with a cyclic automorphism.
The theory of voltage graphs has become a standard tool in the study graphs admitting a semiregular group of automorphisms. We introduce the notion of a cyclic generalised voltage graph to extend the scope of this theory to graphs admitting…
We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the…
This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…
In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries.…
In this paper we consider some global constructions of liftings of automorphic representations attached to some commuting pairs in the exceptional group $F_4$. We consider two families of integrals. The first uses the minimal representation…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
The aim of this book is to show that the use of f-analytic families of finite type cycles (cycles having finitely many irreducible components, but not compact in general) in a given complex space may be useful in complex geometry, despite…
In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…