Complex spherical designs from group orbits. (English) Zbl 1542.05023
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.
Reviewer: Arash Ghaani Farashahi (Wien)
MSC:
| 05B30 | Other designs, configurations |
| 42C15 | General harmonic expansions, frames |
| 65D30 | Numerical integration |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
complex spherical design; unitary group action; complex reflection group; harmonic Molien series; spherical \(t\)-designs; projective designs; complex \(\tau\)-designs; tight spherical designs; finite tight frames; integration rules; cubature rules; cubature rules for the sphere; Weyl-Heisenberg SICSoftware:
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