Complex spherical designs from group orbits
type: Item
instance of: scholarly article
title: Complex spherical designs from group orbits
zbMATH Open document ID: 1542.05023
author: Mozhgan Mohammadpour
author: Shayne Waldron
published in: Journal of Approximation Theory
publication date: 2024-06-23T00:00:00Z
review text: This paper considers the general form of complex spherical designs via orbits of the unitary action of a finite group. It is shown that orbits which have large enough stabilisers are then good candidates for being optimal complex spherical designs. As an application, explicit constructions of some putatively optimal real and complex spherical \(t\)-designs disscussed.
reviewed by: Arash Ghaani Farashahi
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 7870169
zbMATH Keywords: complex spherical design
zbMATH Keywords: unitary group action
zbMATH Keywords: complex reflection group
zbMATH Keywords: harmonic Molien series
zbMATH Keywords: spherical \(t\)-designs
zbMATH Keywords: projective designs
zbMATH Keywords: complex \(\tau\)-designs
zbMATH Keywords: tight spherical designs
zbMATH Keywords: finite tight frames
zbMATH Keywords: integration rules
zbMATH Keywords: cubature rules
zbMATH Keywords: cubature rules for the sphere
zbMATH Keywords: Weyl-Heisenberg SIC
MaRDI profile type: Publication
cites work: Constructing exact symmetric informationally complete measurements from numerical solutions
cites work: Construction of spherical 4- and 5-designs
cites work: Constructions of spherical 3-designs
cites work: Spherical t-designs which are orbits of finite groups
cites work: Q3407104
cites work: On the construction of highly symmetric tight frames and complex polytopes
cites work: Nice error frames, canonical abstract error groups and the construction of SICs
cites work: Spherical designs and finite group representations (some results of E. Bannai).
cites work: Spherical codes and designs
cites work: Q3670063
cites work: Fibonacci-Lucas SIC-POVMs
cites work: Q3972076
cites work: \(t\)-designs with general angle set
cites work: On spherical t-designs in \(R^ 2\).
cites work: Spherical \((t,t)\)-designs with a small number of vectors
cites work: On Weyl-Heisenberg orbits of equiangular lines
cites work: Q3395519
cites work: On a generalization of spherical designs
cites work: Complex Spherical Designs and Codes
cites work: Q3958740
cites work: Q4126536
cites work: Q5730998
cites work: An introduction to finite tight frames
cites work: QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY
cites work: On spherical designs of some harmonic indices
DOI: 10.1016/J.JAT.2024.106047
description: scientific article; zbMATH DE number 7870169