Year: 2025
Type: preprint
Abstract: In this paper, we introduce the framework of a generalized design, which represents any linear operator as a finite sum of local linear maps attached to finitely many points, thereby abstracting the core of design theory without employing integration. We then construct such a design on the space of sections of the tautological bundle over the complex projective line. By using the irreducible decomposition of this space as an SU(2)-representation, we show that the projection onto its lowest-dimensional summand can be realized as a finite sum of these local maps. Our construction relies on invariant theory for the binary icosahedral group and an analysis of fixed-point subspaces in symmetric tensor representations.
Source: arXiv (Cornell University)
Author: Yuya, Ikeda
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416770169
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