Related papers: Hadamard Star Configurations
We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.
A characterization of $\mathbb{Z} _t \times \mathbb{Z}_2^2$-cocyclic Hadamard matrices is described, depending on the notions of {\em distributions}, {\em ingredients} and {\em recipes}. In particular, these notions lead to the…
In this paper, we prove the conjecture posed by Keller and Rosemarin at Eurocrypt 2021 on the nullity of a matrix polynomial of a block matrix with Hadamard type blocks over commutative rings of characteristic 2. Therefore, it confirms the…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
We find the minimal free resolution of the ideal of a star-configuration in $\mathbb{P}^n$ of type $(r,s)$ defined by general forms in $R=\Bbbk[x_0,x_1,\dots,x_n]$. This generalises the results of \cite{AS:1,GHM} from a specific value of…
We propose a new method to infer the star formation histories of resolved stellar populations. With photometry one may plot observed stars on a colour-magnitude diagram (CMD) and then compare with synthetic CMDs representing different star…
We study $m \times n$ matrices whose columns are of the form \[\{(a_{1j},\ldots, a_{nj}): \quad a_{1j} = \lambda_j,\ a_{ij} = \pm\lambda_j\ , \ \lambda_j >0 ,\ j=1,2,\ldots,n\}.\] We explicitly construct for all $a = (a_1,\ldots,…
Complex Hadamard matrices have received considerable attention in the past few years due to their appearance in quantum information theory. While a complete characterization is currently available only up to order 5 (in \cite{haagerup}),…
Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the usual star product of exponential type becomes continuous.…
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean…
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…
We show that given a stable weighted configuration on the asymptotic boundary of a locally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration if the configuration is stable. Moreover,…
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard…
Hadamard matrices of order $n$ are conjectured to exist whenever $n$ is $1$, $2$, or a multiple of $4$; a similar conjecture exists for skew Hadamard matrices. We provide constructions covering orders $\le 1208$ of all known Hadamard and…
The ranks and kernels of generalized Hadamard matrices are studied. It is proven that any generalized Hadamard matrix $H(q,\lambda)$ over $F_q$, $q>3$, or $q=3$ and $\gcd(3,\lambda)\not =1$, generates a self-orthogonal code. This result…
By employing the external Kasparov product, Hawkins, Skalski, White and Zacharias constructed spectral triples on crossed product C$^\ast$-algebras by equicontinuous actions of discrete groups. They further raised the question for whether…
We study the existence and construction of circulant matrices $C$ of order $n\geq2$ with diagonal entries $d\geq0$, off-diagonal entries $\pm1$ and mutually orthogonal rows. These matrices generalize circulant conference ($d=0$) and…
In this paper we present new Hadamard matrices and related combinatorial structures. In particular, it is constructed 5202 inequivalent Hadamard matrices of order 36 as well as 180538 Hadamard symmetric designs with 35 points in addition to…
We present a new method for constructing affine families of complex Hadamard matrices in every even dimension. This method has an intersection with the Di\c{t}\u{a} construction and it generalizes the Sz\"oll\H{o}si's method. We reproduce…
We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by the Welch bound whenever a skew Hadamard of order $d+1$ exists. Our proof uses a variant of Hadamard doubling that converts any equiangular tight frame of size…