There are no extremal eutactic stars other than root systems
Number Theory
2024-10-30 v2
Abstract
A eutactic star on an integral lattice is called extremal if it induces a holomorphic Jacobi form of lattice index and singular weight via the theta block. The famous Macdonald identities imply that root systems are extremal as eutactic stars. In this paper we prove that every extremal eutactic star arises as a root system. This answers a question posed by Skoruppa.
Cite
@article{arxiv.2302.00184,
title = {There are no extremal eutactic stars other than root systems},
author = {Haowu Wang},
journal= {arXiv preprint arXiv:2302.00184},
year = {2024}
}
Comments
6 pages, to appear in Bulletin of the London Mathematical Society