Designs on the Tautological bundle
Combinatorics
2025-11-26 v1 Representation Theory
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.
Cite
@article{arxiv.2511.20114,
title = {Designs on the Tautological bundle},
author = {Ikeda Yuya},
journal= {arXiv preprint arXiv:2511.20114},
year = {2025}
}